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Mars Inc claims that they produce M&Ms with the following distributions:Brown 30% Red 20% Yellow 20% Orange 10% Green 10% Blue 10%bag ofM&Ms was randomly se...

Question

Mars Inc claims that they produce M&Ms with the following distributions:Brown 30% Red 20% Yellow 20% Orange 10% Green 10% Blue 10%bag ofM&Ms was randomly selected from the grocery store shelf; and the color counts Were:Broun 21 Red 23 Yellow 19 Orange 16 Green 16 Blue 14Find the 9890 confidence interval for the proportion of orange M&Ms in that bag:a) 0 [0.068, 0.026]b) 0 [0.068, 0.226][0.118, 0. .123]d) 0[-0.032. 0.176]e) 0[-0.012,0.226]0None of the aboreReview Later

Mars Inc claims that they produce M&Ms with the following distributions: Brown 30% Red 20% Yellow 20% Orange 10% Green 10% Blue 10% bag ofM&Ms was randomly selected from the grocery store shelf; and the color counts Were: Broun 21 Red 23 Yellow 19 Orange 16 Green 16 Blue 14 Find the 9890 confidence interval for the proportion of orange M&Ms in that bag: a) 0 [0.068, 0.026] b) 0 [0.068, 0.226] [0.118, 0. .123] d) 0[-0.032. 0.176] e) 0[-0.012,0.226] 0None of the abore Review Later



Answers

M\&M Colors. Observing that the proportion of I3.29 Mam Colors. blue M\&Ms in his bowl of candy appeared to be less than that of the other colors, R. Fricker, Jr., decided to compare the color distribution in randomly chosen bags of M\&Ms to the theoretical distribution reported by M\&M/MARS consumer affairs. Fricker published his findings in the article "The Mysterious Case of the Blue M\&Ms" (Chance, Vol. 9(4), pp. 19-22). The following is the theoretical distribution. $$\begin{array}{l|c} \hline \text { Color } & \text { Percentage } \\ \hline \text { Brown } & 30 \\ \text { Yellow } & 20 \\ \text { Red } & 20 \\ \text { Orange } & 10 \\ \text { Green } & 10 \\ \text { Blue } & 10 \\ \hline \end{array}$$ For his study, Fricker bought three bags of M\&Ms from local stores and counted the number of each color. The average number of each color in the three bags was distributed as follows.

So again, according to the manufacturer of Eminem's, he has given us a distribution that the Eminem should follow based on various colors. So let's just draw the observation table. This is always the first step. So the first one is color. All right. So what are the various colors that we have? Okay, so we have brown, yellow, red, blue, orange and cream. Okay. Mhm. So we have brown. Hello, red, blue, orange and screen. Okay then we have the observed values. That is 53 66. So, let us just right. This is the frequency as it is given to us Because this is 53. This is 66, 38 96 88. 59 38 96 88 59. Okay. All right. So what we have over here Is that there is a boy now he counted the number of Eminem's that were each color and obtained the frequencies that are giving us at the table. Now, what we have to do is we have to test whether the Peanut M&M's follow the distribution stated by Eminem Mars at 0.05 level of significance. Okay, so our alpha, 0.05 Alpha is 0.05. Okay, what is a null hypothesis? This is the first step of solving this question. Finding on the hypothesis. The null hypothesis is that the peanut Eminem's follow the distribution stated by Eminem mars. Okay, the peanut Eminem's follow the distribution. Follow the distribution given by Eminem s are given by the manufacturer. Given by the manu factor. All right. What is going to be the alternative hypothesis? Now, that is just checking the textbook is the name of the manufacturer, eminent mars. Okay, so a minute mark is the manufacturer. Alright, this will be that the peanut Eminem's the peanut m and m's do not follow the distribution given by Eminem mars. All right, so now we have the number and the alternative hypothesis in place. What is the next step? The next step is to calculate the expected values. But first we need the probabilities. What is the distribution that we have? The probabilities? The probabilities. Okay, so the probabilities are 15 Brown. So this should be .15 15 brown. Oh, just a moment. This is 15 yellow. Actually, what is for brown? It's 12 brown. 15 yellow. Okay, so this is 12 brown. This is 15 hello, 12 red, 23 blue. 12 red, 23 blue, 23 orange and 15 Green 23 audience and 15 cream. Okay, so this is 12, 15 12, 23 23 and 15. Okay, now, the next step is finding the expected values, the expected values. Now how do you calculate the expected values? Expected value for any categories given by the sample says? The sample says multiplied by the probability for that category, multiplied by the probability four. Category I Okay, so this is going to be sample size, multiplied by the probability for category. Now what is a sample says in order to find the sample says we need to add this frequency table. So if I had all of the 53-plus 6 86 plus 38 plus 96 plus 88 That's 15 9. When is this? 404? That is just check this with a calculator. So this is 50. c 2015 three plus 66 plus 38 plus 96 plus 88-plus 59. Yes, this is 400. My apologies. This is 400. Okay, now how do you find the expected values? Let's say for brown it will be The sample size. That is 400. multiplied by the probability, right? Because if the peanut Eminem's actually one of the probability is given by the manufacturer, 12 of 400 Should be brown colour, so this is nothing but 48, the expected value is 48. In this case it is 60, This is again 48. Now, 23, this has to be 92. This also has to be 92 and this has to be 16 again, right? 48 60 48 90-92 and 60 years. This is 400. So now that we have the expected values, what is the next step? The next step is to calculate the chi square statistic. How do you calculate the chi square statistic? Now, for every category, if we are going to find the difference and observed and expected values will square them. Then we'll divide this result by the expected values and in the end we'll add all of these values for all the categories. So let us look at this now in this column four category, Brown, What is the difference in observer, unexpected values. 53 -48, which is five, the square of five is 25. And we divided by the expected value 48, which is .5-0. So this is .5208. All right now the difference is 66 squares 36 divided by the expected value of 16, Which gives us .6. Okay then the difference is 10 10 squares 100 100 Divided by the expected value of 48 gives us 2.083. So this is 2.083. All right now the difference is 44 squared 16 Divided by the expected value of 92. 1.1739. Let's just write this is .174. Now the defense is again for In this case, force for a 1616 divided by the expected value of 92. Well give us .174 again .174 For the last one. The difference is 11 divided by 60 One square is again one. And this dude was 16. Will give me .0166 .0166. Okay, now what I do is add all of these up. So this is going to be .5208 Plus four in 6 plus 2.083 plus .174 plus .174 plus 0.0166. This is 3.5684. So my guys wasted a stick these 3.568 four. Right, is this right? Well, this looks to be correct. Okay, so now the next step is I have the chi square statistic. Now, in order to continue my analysis, I need one very important piece of information, which is called the degrees of freedom. And this is given by the formula number of categories minus one. Right, Okay. So how many categories do I have? Brown, yellow, red, blue, orange, green. I have six categories. So this will be 6 -1, which will give me five. So my degrees of freedom is fighting. All right. Now, in order to continue my analysis, I have two approaches. The first one is the p value approach. The p value approach. Okay. And the second approach is the critical value approach. The critical value approach. All right, so how do I find a P value? I have my chi square statistic as 3.5684 I have My degrees of freedom is fine. Now I can either use the chi square table or I can use a calculator. Our statistical package. So what I have here is an online tool calculator. I put on my chi square value at 3.56843 point 5684 My reviews of freedom is five. My level of significance is 0.05 and my p value is .6130. My p value, My p value is 0.6130 0.6130. My alpha was 0.5 Now I reject the null hypothesis if my p value is less than alpha, but in this case my p value is greater than alpha. Hence I feel to reject my null hypothesis. Each not great. Okay, now how about the critical value approach? Now this time I just need two pieces of information, My alpha, which happens to be 0.05 and my degrees of freedom, it happens to be five. Now I will use a critical value calculator. I put in my al 50.5 my degrees of freedom as five. And I get my critical value as 11.7 So my critical value, my critical Value is 11.07. What does this mean? Let's say that this is my chi square graph. Right? We know that the graph for the chi square distribution changes with various degrees of freedom. Right? So let's say that this degrees of freedom is five. This might not be accurate, but it is enough for understanding Now, critical value is 11.07. So let's say that this is 11.07. So all the values that lie to the right of this value will be set to be in the rejection region, right? So I will reject all the values that lie to the right of this. Okay, what is the value that I have? The value that I have is 3.5684, which lies to the left, which may lie somewhere around here. I don't know. It may be here or here or here, But it lies to the lab. So this is three 5684 right to the left of it. And this does not line the rejection region and hence I will fail to reject my hypothesis. It's not which is the same answer that we got over here and that we should get because these are just two different approaches. The answer has to be the same, right? So in this case, what we can say is add 0.05 level of significance level of significance. We do not have enough statistical enough statistical evidence, enough statistical evidence to suggest, do suggest that now we are okay to suggest that the claim of the company, that claim of the manufacturer M and M mars of the manufacturer of the manufacturer is false, right, is false or is not correct. So we can say that the peanut M and M's that we have do actually follow the distribution that is given by the eminent manufacturer right? We are not accepting the new hypothesis. But what we are saying is we do not have enough statistical evidence to reject it. Okay, so the first step in solving this question was to come up with the null and alternative hypotheses. National hypothesis was that the peanut M and M's follow the distribution given by the manufacturer. The alternative was that the peanut M and M's do not follow the distribution given by the manufacturer Eminem mars. Then we went to the table, right? The frequency distribution table. So over here we have the frequencies, we have the probabilities. We calculated the expected values using this formula way. And after that we apply this formula to get the chi square statistic which came out to be 3.5684 The another very important piece of information or isIL analysis is the degrees of freedom, which is a number of categories minus one, which is five in our case. Then we went on to solve this question by two different approaches. You can use any one of these, but it's better to know both of them. So I explained both of those approaches. And in the end we came to the conclusion that we do not have enough statistical evidence to reject. Then I'll hypothesis. Right? So we do not have enough statistical evidence to suggest that the claim of the manufacturer is fonts. Okay, This is how we go about doing this question.

Okay, so let us look at this question. Now, this question says that according to the manufacturer of Eminem's 13 of the plane and the lives in the back should be brown. And then you have different percentages for yellow, red, blue, orange and green. Okay, so let's just look at the table that we have the first and the foremost thing we should do while solving a chi square problem is draw the table. So we have colors and then we have frequency. They observed frequency. This is frequency. All right, so the different colors that we have, our brown, yellow, red, blue, orange, green. So this is brown, yellow, fred blue, orange and green. All right. Now, What are the observed frequencies that we have 61, 64 54, 61 64, 54 61, 96 64 61 96. And then we have 164 oh shape. So a student randomly selected a bag of plain Eminem's he got at the number of Eminem's. Right. And this is the frequency that we have the frequency table. Now, what we have to do is we have to test whether the plane Eminem's follow the distribution stated by the Eminem mars. Okay. 13 of plain eminem's in a bag. Should be proud on. All right. Okay. So our alpha is 0.05. This is a simple question. Piece of alpha. Mm mm. Okay, what is happening? Yeah. So this, for some reason is not working, but Okay, we'll make it work. So Alpha. Okay, where is this not working? Just a moment, guys, just bear with me, this should not happen. Mhm. Mhm. Okay. Yeah, it's works. So antifa is 0.05 relations. Now, what is the null hypothesis? The null hypothesis h not. Is going to be that the plane evidence for distribution stated by the M and M mars, Okay. That the plane M. N. M. S follow the distribution given by the manufacturer. Eminem mars given goodbye mm mm. How do you write this? Eminent mars? Okay, I think this is a manufacturer. What is going to be the alternative hypothesis? The alternative hypothesis will be that the plane Eminem's M and M's don't follow the distribution given by mm mm mars. Alright, now what we have with us different categories and the observed frequencies. So from the observed frequencies, what we can do is we can find the sample size, right? What's the sample size? It is going to be the addition of all of these frequencies. So let me do one thing. Let me take the calculator. Let me add all of these 61 plus 64 plus 54 plus 61 plus 96 plus 64 which is 400. So this is 400. Okay. Now what are the probabilities? What are the probabilities? Right. What are the probabilities? The manufacturer says that 13 should be brown. Right? So this should be 13 or let me get this is .13, 14 should be yellow. 13 should be dead. So yellow is 14 point when four, red is 0.13 24 Blue, 20 Orange. So this is 24 blue, 20 orange And 16 should be green. So this is .16. Okay. Now, in order to conduct the chi square test, we need to find what is known as the expected values. Right? We need to find what are the expected values. If the Eminem actually followed this distribution, this distribution in this column. So how do you find that expected values? Let us come down here. Expected values for any category are given by the sample says which is 400 and Archies. The sample size multiplied by the probability for each category, multiplied by the probability probability for each category, or for category I in this case. Right. Because we are finding e I expected value for the category. So let us apply this formula here. Now I have 400. So what is the probability For brown at a 0.1? So what should be the expected value? 13 of 400 should be brown. Okay, So 13 of 400 is what? This is 52 if I'm not wrong. Yes. So this is 52. Yes. Similarly, this will also become 52. Now this is 14. Right? So 14 of 456. Okay, point to point to is for 400 rate. They should be 80 A .2 for what will be .24. So this is going to be 24 into four, which is nothing but 96 96. Okay. And .16. So this is four into 16. Which happens to meet 64. Right? Yeah, this is 64. All right. Now that we have the expected values now, we have to calculate the chi square statistic. And what is the formula for that? To calculate the chi square statistic for every category you do this computation, you find the difference between the observer and the expected value. You square. The difference divide the difference by the expected value. And after doing this for all the categories, you simply sunk them all up. So this is what you are going to do here. Let us look at this formula in action. So, the first category is brown. Right? So what is the difference between the observed frequency and the expected frequency? 61 -52 happens to be 99 square is 81 81 divided by the expected value, which is 52. This gives me 1.5576 So this is 1.5576. They then eight squared is 64. The difference for yellow 64 minus 56 which is eight, It's square is 64. And you divide this by the expected value is 56. So this is 1.1428 1.1428. Then the difference for red is 50 for -52, which happens to be too. You divided by the expected value. That is 52. You get just want, So this is the square is four and you divide this by 52, you get 0.0769. Let me just read this is 0.08 For blue. It is going to be 96 -61. You square this 35 square is one to do five in a divided by 96. So this is 12.76, 12.76. The difference between 96 and 80 Is 16, you square this to 56 and divided by the expected value of 80. This is 3.2, then for the last one, the expected and they absorb frequencies are the same. So this will be zero. Now what I will do is I will add all of these up. So this is 1.5567, 1.5576 1.5576 plus 1.142, 8, 0.8 plus 12.76 plus 3.2 Plus year. So this is 18.7404. So archives quested a steak Turns out to be 18.740 food. All right now I have my guys question is sick now, what else do I want now? I want to find the degrees of freedom. This is the next step. Degrees of freedom is given by the formula number of categories. Number of categories minus one. So how many categories do I have? Brown, yellow, red, blue, orange, green. So I have six different categories. So this is going to be 6 -1, which is fine. All right. Now, in order to continue with my analysis, I can use to approach is the first one is the P value approach. The p value approach in which we will find the P value and compare it with alpha to reach a conclusion. And the other one is the critical value approach. The critical value approach. Okay, how do I find the P value for this? I can either use the chi square table. All I can use an online calculator or a statistical package like R. Or X. Or something like. So I have my chi square value is 18.74 and my degrees of freedom was five. So 18.74. I put in my chi square value. This is 18.74° of freedom happens to be five. My level of significance 0.05 and I hit calculate right? So what I get is My P Value 0.002149. So my p value, my p value is 0.2149 What was my alpha phi Alpha was 0.5 I can clearly see that my P value is less than alpha hands. I can say that I will reject My nail hypothesis. H. nine. Now how can I use the critical value approach? Critical value approaches? I'm just going to find the critical value for my alpha of 0.05. My alpha of 0.05. And my degrees of freedom five. This is an increase of freedom, right? So I can use a critical value calculator. My alpha 0.5 My degrees of freedom happened to be five and I hit calculate And I get 11.07. My critical value. My can you take a Value is 11.07. Right? So if this is my chi square graph right, we all know that this is skewed 11.07 Let's say lies somewhere around here. And the reason to the right of this is the rejection region. So any value that I get That is greater than 11.07 lies in the rejection region. What is the value that I have? My values 18.74, which definitely lies to the right? So let's say it lives somewhere around here 18.7404. And this lies in the rejection reason. Hence I will reject final hypothesis, which is what we got from the first method as well as we should. Right? So we will reject the null hypothesis. Or we can say that at 5% right and 5% 11 of significance of significance. We have enough statistical evidence to suggest that. And just look at the question, what was the wording? According to the manufacturer of Eminem's 13 of this? This. Okay, so he has given us the frequency distribution test whether the plane Eminem's follow distribution stated by Eminem mars suggest that the plane Eminem's the plane came in. Ems don't or let's say do not do not follow the distribution suggested by the company by the manufacturer, which happens to be Eminem mars in this case by Eminem mars. Right? So their claim Can be falsified, right? We will say that at 0.05 level of significance, we have enough statistical evidence to suggest that the plane Eminem's do not follow the distribution that is suggested by the manufacturers. This is how we go about doing this question. Now, this is a very simple question. Just a little lengthy. The reason is we had to calculate the expected values by using this formula where right and in the area to get rid of the guys can statistic. Hence, it was a little lengthy in calculation, coming up with in Orlando alternative hypothesis. Very simple. And after this we followed two approaches, and we found that the answer is the same from both of these approaches, p value as well as critical value approach as it should be, and in the end we end up rejecting Arnold hypothesis.

Okay, so let us look at this question. Now, this question says that according to the manufacturer of Eminem's 13 of the plane and the lives in the back should be brown. And then you have different percentages for yellow, red, blue, orange and green. Okay, so let's just look at the table that we have the first and the foremost thing we should do while solving a chi square problem is draw the table. So we have colors and then we have frequency. They observed frequency. This is frequency. All right, so the different colors that we have, our brown, yellow, red, blue, orange, green. So this is brown, yellow, fred blue, orange and green. All right. Now, What are the observed frequencies that we have 61, 64 54, 61 64, 54 61, 96 64 61 96. And then we have 164 oh shape. So a student randomly selected a bag of plain Eminem's he got at the number of Eminem's. Right. And this is the frequency that we have the frequency table. Now, what we have to do is we have to test whether the plane Eminem's follow the distribution stated by the Eminem mars. Okay. 13 of plain eminem's in a bag should be brown. All right, Okay. So our alpha is 0.05. This is a simple question. Piece of alpha. Mm mm. Okay, What is happening? Yeah. So this, for some reason is not working, but Okay, we'll make it work. So Alpha. Okay, where is this not working? Just a moment, guys, just bear with me, this should not happen. Mhm. Mhm. Okay. Yeah, it's works. So an alpha is 0.05 relations. Now, what is the null hypothesis? The null hypothesis h not. Is going to be that the plane evidence for distribution stated by the M and M mars, Okay. That the plane M. N. M. S follow the distribution given by the manufacturer. Eminem mars given Goodbye mm mm. How do you write this? Eminent mars? Okay, I think this is a manufacturer. What is going to be the alternative hypothesis? The alternative hypothesis will be that the plane Eminem's M and M's don't follow the distribution given by mm hmm mars. Alright, now what we have with us different categories and the observed frequencies. So from the observed frequencies, what we can do is we can find the sample size, right? What's the sample size? It is going to be the addition of all of these frequencies. So let me do one thing. Let me take the calculator. Let me add all of these 61 plus 64 plus 54 plus 61 plus 96 plus 64 which is 400. So this is 400. Okay. Now what are the probabilities? What are the probabilities? Right. What are the probabilities? The manufacturer says that 13 should be brown. Right? So this should be 13 or let me get this is .13, 14 should be yellow. 13 should be dead. So yellow is 14 point when four, red is 0.13 24 Blue, 20 Orange. So this is 24 blue, 20 orange And 16 should be green. So this is .16. Okay. Now, in order to conduct the chi square test, we need to find what is known as the expected values. Right? We need to find what are the expected values. If the Eminem actually followed this distribution, this distribution in this column. So how do you find that expected values? Let us come down here. Expected values for any category are given by the sample says which is 400 and Archies. The sample size multiplied by the probability for each category, multiplied by the probability probability for each category, or for category I in this case. Right. Because we are finding e I expected value for the category. So let us apply this formula here. Now I have 400. So what is the probability For brown at a 0.1? So what should be the expected value? 13 of 400 should be brown. Okay, So 13 of 400 is what? This is 52 if I'm not wrong. Yes. So this is 52. Yes. Similarly, this will also become 52. Now this is 14. Right? So 14 of 456. Okay, point to point to is for 400 rate. They should be 80 A .2 for what will be .24. So this is going to be 24 into four, which is nothing but 96 96. Okay. And .16. So this is four into 16. Which happens to meet 64. Right? Yeah, this is 64. All right. Now that we have the expected values now, we have to calculate the cais question to stick. And what is the formula for that? To calculate the chi square statistic for every category you do this computation, you find the difference between the observer and the expected value. You square. The difference divide the difference by the expected value. And after doing this for all the categories, you simply sum them all up. So this is what you are going to do here. Let us look at this formula in action. So, the first category is brown. Right? So what is the difference between the observed frequency and the expected frequency? 61 -52 happens to be 99 square is 81 81 divided by the expected value, which is 52. This gives me 1.5576 So this is 1.5576. They then eight squared is 64. The difference for yellow 64 minus 56 which is eight, It's square is 64. And you divide this by the expected value is 56. So this is 1.1428 1.1428. Then the difference for red is 50 for -52, which happens to be too. It divided by the expected value. That is 52. You get just want, So this is the square is four and you divide this by 52, you get 0.0769. Let me just read this is 0.08 For blue. It is going to be 96 -61. You square this 35 square is one to do five in a divided by 96. So this is 12.76, 12.76. The difference between 96 and 80 Is 16, you square this to 56 and divided by the expected value of 80. This is 3.2, then for the last one, the expected and they absorb frequencies are the same. So this will be zero. Now what I will do is I will add all of these up. So this is 1.5567, 1.5576 1.5576 plus 1.142, 8, 0.8 plus 12.76 plus 3.2 Plus year. So this is 18.7404. So archives quested is steak, Turns out to be 18.740 food. All right now I have my guys question is sick now, what else do I want now? I want to find the degrees of freedom. This is the next step. Degrees of freedom is given by the formula number of categories. Number of categories minus one. So how many categories do I have? Brown, yellow, red, blue, orange, green. So I have six different categories. So this is going to be 6 -1, which is fine. All right. Now, in order to continue with my analysis, I can use to approach is the first one is the P value approach. The p value approach in which we will find the P value and compare it with alpha to reach a conclusion. And the other one is the critical value approach. The critical value approach. Okay, how do I find the P value for this? I can either use the chi square table. All I can use an online calculator or a statistical package like R. Or X. Or something like. So I have my chi square value is 18.74 and my degrees of freedom was five. So 18.74. I put in my chi square value, This is 18.74° of freedom happens to be five. My level of significance 0.05 and I had to calculate right? So what I get is My P Value 0.002149. So my p value, my p value is 0.2149 What was my alpha phi alpha was 0.5 I can clearly see that my P value is less than alpha hands. I can say that I will reject My nail hypothesis. H nine. Now how can I use the critical value approach? Critical value approaches? I'm just going to find the critical value for my alpha of 0.05. My alpha of 0.05. And my degrees of freedom five. This is an increase of freedom, right? So I can use a critical value calculator. My alpha 0.5 my degrees of freedom happened to be five and I hit calculate And I get 11.07. My critical value my can you take a Value is 11.07 Right? So if this is my chi square graph right? We all know that this is skewed 11.07 Let's say lies somewhere around here. And the reason to the right of this is the rejection region. So any value that I get That is greater than 11.07 lies in the rejection region. What is the value that I have? My values 18.74, which definitely lies to the right? So let's say it lives somewhere around here 18.7404. And this lies in the rejection reason. Hence I will reject final hypothesis, which is what we got from the first method as well as we should. Right? So we will reject the null hypothesis. Or we can say that at 5% right and 5% 11 of significance of significance. We have enough statistical evidence to suggest that. And just look at the question, what was the wording? According to the manufacturer of Eminem's 13 of this? This. Okay. So he has given us the frequency distribution test whether the plane Eminem's follow distribution stated by Eminem mars suggest that the plane Eminem's the plane came in. Ems don't or let's say do not do not follow the distribution suggested by the company by the manufacturer, which happens to be Eminem mars in this case by Eminem mars. Right. So their claim Can be falsified, right? We will say that at 0.05 level of significance, we have enough statistical evidence to suggest that the plane Eminem's do not follow the distribution that is suggested by the manufacturers. This is how we go about doing this question. Now, this is a very simple question. Just a little lengthy. The reason is we had to calculate the expected values by using this formula where Right and in the area to get rid of the guys can statistic. Hence, it was a little lengthy in calculation, coming up with in Orlando alternative hypothesis. Very simple. And after this we followed two approaches, and we found that the answer is the same from both of these approaches, p value as well as critical value approach as it should be, and in the end we end up rejecting Arnold like boxes.

After everyone. So we will be solving location number 25. In this question, we have given the distribution of different colors that Eminem candy bar Candy Powers has. So the colors are brown, yellow, red, orange, green, blue. And the frequencies of these colors in the Eminem candy um Gallagher it's been given. So as a part, we have to find out the relative frequencies for these colors firstly we will just write the different colors that he has as our classes, frequency is being given to us and we have to find the relative frequency. No, For the crown fun frequencies Cuban 1 52 military creates total frequency. It is 509. That's the total number of observations. Similarly, we can just input the frequencies for different colours has fell in the street to include the relative frequency. Let's say. We have to check with relative frequency for the brown color. We will just divide 152 by the total number of observations, status 509. And the result comes out to be .299 as the relative frequency for the brown colour. Similarly, we can find all other relative frequencies just by dividing the number of observations for particular color And divided by the total number of observations. That is 509 and the total sum of relative frequency we will get as one. So here we can just find real efficiency for all and we can add all the radio frequencies and check our older answers of re deficiencies are correct or not. If that's a musical to one means we have done it rightly. I will just input the religions of all these colors, which I found out. You can calculate by your own and match whether you're getting the right or not. Okay, so we have calculated the religion frequency for all the colors. The next part will move on to building a pie chart for the pie chart. We will just multiply the relative frequency for each of the color into 3 60 degrees. This will give us the degree. We have to plot for all the classes on the pie chart. Let's say for example, we will calculate every degrees need required for the blue color. It will be .084 into 360°.. That will come out to be 30.2430. Now report this particular degree on the pipe by charge. Let's say this is the blue color we have given and the angle of this particular flu bi will be 30.24 degrees. Similarly, we will just float all the other classes as well in the pie chart. Next they will move to the C. Part that is plotting a burchard. The bar chart will plod lady frequency on the boxes and our classes color in this case on the X axis. Let's say we will blood a bar chart for well just brought a single virtue for let's say do killer. So this particular value would be .084. That is the relative frequency of the blue color. Similarly, we will applaud the other bars has felt for all the other different colors. Just related frequency on the Y axis. Thank you. Have a good day.


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Pb? (aq)7 Pb(s)-0.1266,n6 - (-u. / 6 ) |+1.274 V ~0.637 +0.8890.889 40.637 V29. concentration cell is constructed by using the same half-reaction for both the cathode and anode. What is the value of Ecell for concentration cell that combines silver electrodes in contact with 0.10 M silver nitrate and 0.00003 M silver nitrate solutions? +0.80 V for AgAgt) +0.21 -0.21 +0.59 V +1.01 V +0.80 V
Pb? (aq) 7 Pb(s) -0.126 6,n6 - (-u. / 6 ) | +1.274 V ~0.637 +0.889 0.889 40.637 V 29. concentration cell is constructed by using the same half-reaction for both the cathode and anode. What is the value of Ecell for concentration cell that combines silver electrodes in contact with 0.10 M silver nitr...
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Question 90 (1 point) The template for protein synthesis isthe primary transcript:mRNArRNAtRNA
Question 90 (1 point) The template for protein synthesis is the primary transcript: mRNA rRNA tRNA...
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Select the statement that is NOT correctUMConfigurationsBased on the above PEC diagram describing mixing of two compounds(M= Mixed/Dissolved state; UM-Unmixed/ Undissolved state)The two molecules have very different dominant intermolecular forcesHigher temperatures will favor more mixed stateLower temperature will lead t0 more unmixing of the two moleculesQ Search or type URL
Select the statement that is NOT correct UM Configurations Based on the above PEC diagram describing mixing of two compounds (M= Mixed/Dissolved state; UM-Unmixed/ Undissolved state) The two molecules have very different dominant intermolecular forces Higher temperatures will favor more mixed state ...
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Problem 4. Rigid object at equilibrium. (30 points) A 5m long diving board of negligible mass is supported by pillar (ful- and bolt as in the figure The bolt is at the left end of the diving crum) board, the fulcrum is at 1.5 I from the left end: Find the forces exerted by the fulcrum and bolt when 90 kg diver stands at the right end of the board:O-odve 90 *5GJ = 4oky 4 6) 882ASm
Problem 4. Rigid object at equilibrium. (30 points) A 5m long diving board of negligible mass is supported by pillar (ful- and bolt as in the figure The bolt is at the left end of the diving crum) board, the fulcrum is at 1.5 I from the left end: Find the forces exerted by the fulcrum and bolt when ...
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Given that quantity Q(t} exhibiting exponential decay is described by the function1800e J,oQ(t) where is measured in years answer the following questions_ What is the decay constant k?What quantity is present initially? unitsComplete the following table of values. (Round your answers to the nearest whole number:)100
Given that quantity Q(t} exhibiting exponential decay is described by the function 1800e J,o Q(t) where is measured in years answer the following questions_ What is the decay constant k? What quantity is present initially? units Complete the following table of values. (Round your answers to the near...
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Find and classify all of the singularities to the following function: If the singularity is pole, then what is its order? Justily your answer_2i - 1) sin ' 7(2+1)f(-)
Find and classify all of the singularities to the following function: If the singularity is pole, then what is its order? Justily your answer_ 2i - 1) sin ' 7(2+1) f(-)...
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~eannm Sercpii 71Pon/ HsSuamnctananneoCraclong the Cune path shovin the figure0 (nesum? that theant'mo-ionDarzllaI~axis ardits Finz motionthe X-axis> (m)0.150 ms0.4100.150 m/s0.150(m)0.1000.450znt $ positions and velocities are indicateC tor timesand [ =Determinecomponentsthe ants fisplacement averaqe velogty znd averaqe acceleration Detween the two umesHIMIdisplacement (In m)averaje Yelccicy Uin m'3Yav,%averaje acceleration (in m/s2) m's2 324% m/s?
~eannm Sercpii 71Pon/ HsSuamnctananneo Crac long the Cune path shovin the figure 0 (nesum? that theant' mo-ion Darzlla I~axis ardits Finz motion the X-axis > (m) 0.150 ms 0.410 0.150 m/s 0.150 (m) 0.100 0.450 znt $ positions and velocities are indicateC tor times and [ = Determine components...
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Find the curvature $K$ of the plane curve at the given value of the parameter. $mathbf{r}(t)=5 cos t mathbf{i}+4 sin t mathbf{j}, quad t=frac{pi}{3}$...
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Explain what the student did wrong when simplifying the given expression. Give the correct simplified expression.$$5^{-2} a^{3} b^{-6}$$
Explain what the student did wrong when simplifying the given expression. Give the correct simplified expression. $$5^{-2} a^{3} b^{-6}$$...
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Ccmauta th8 cobiicierts icr tn8 les2t equar02 regrezsion 6qualicn &7d wit8 ihe 6quation; givan tn8 gample slaiisiicz belor {e60,%5210,& 60,& {70,T =0.6,n = &0 #-D-D (Round four dacimal places n2aded: )
Ccmauta th8 cobiicierts icr tn8 les2t equar02 regrezsion 6qualicn &7d wit8 ihe 6quation; givan tn8 gample slaiisiicz belor {e60,%5210,& 60,& {70,T =0.6,n = &0 #-D-D (Round four dacimal places n2aded: )...
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Aajr =Usa: umplmern_Usa: "pifzt24Tatk: 3FFORE jelezr dinaypotei aor tha Reaal -oI =axpl-Tldz#_ baMediz i 3 keat Colert tbe daa Seeiyur dlain 1 gpportadEepet UEClzxDaakTotal nbe 3e bekr; #l- pr bpteized nadianTaTzbCriiTakCorhurzSample iden:Eanng &Aradery Arard Wmig Mxzes Salar cfMBM?Ciora= Jnditt=abudcainFad& Irir; urrr B708 rtVLGramcabraurigebediar cre1l
Aajr = Usa: umplmern_ Usa: "pifzt24 Tatk: 3FFORE jelezr dinaypotei aor tha Reaal -oI =axpl-Tldz#_ baMediz i 3 keat Colert tbe daa Seeiyur dlain 1 gpportad Eepet UE Clzx Daak Total nbe 3e bekr; #l- pr bpteized nadian TaTzb CriiTak Corhurz Sample iden: Eanng &Aradery Arard Wmig Mxzes Salar cf...
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50 credit card holders are randomly selected and the amountsthey currently owe are recorded. The researchers then find the meanand median.The largest data value ($50,000) in the setis then replaced with $1,000,000 and thestatistics are calculated again.a) how much of an effect will this change have onthe mean?b) how much of an effect will this change have onthe median?
50 credit card holders are randomly selected and the amounts they currently owe are recorded. The researchers then find the mean and median. The largest data value ($50,000) in the set is then replaced with $1,000,000 and the statistics are calculated again. a) how much of an effect will this change...
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Fill in the blanks: is a quantitative scale, 5 where there is a true zero point (Li; 1)interval scaleordinal scalenominal scaleRatio scale
Fill in the blanks: is a quantitative scale, 5 where there is a true zero point (Li; 1) interval scale ordinal scale nominal scale Ratio scale...
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Question 24 Find lim x2 'In(?) _ X-0Thc limit docs not exist.d) 0Review Later04
Question 24 Find lim x2 'In(?) _ X-0 Thc limit docs not exist. d) 0 Review Later 04...
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A circuit is constructed with four resistors one inductor; one battery and switch as shown. The values for the resistors are: Ri R2 50 02, R3 = 79 0 and R4 68 0. The inductance is L = 583 mH and the battery voltage is V = 24 V:Ra
A circuit is constructed with four resistors one inductor; one battery and switch as shown. The values for the resistors are: Ri R2 50 02, R3 = 79 0 and R4 68 0. The inductance is L = 583 mH and the battery voltage is V = 24 V: Ra...
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Wnat Isthe product from the following reaction sequence?1. NaNH; CH;CH Br Pdic Zhppd Zn(Cu)
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016 (part 1 of 2) 10.0 pointsAssume that in interstellar space the distance between two electrons is about 0.55 CIn The electric force between the two clectrons 381 repulsive2.attractive.017 (part 2 of 2) 10.0 pointsCalculate the electric force betwecn these two electIOns. The value of the Coulomb constant 9 / 109 N In2 /C2 and the elemnental charge is 6 X 10 19 C Answer i Uits of Na
016 (part 1 of 2) 10.0 points Assume that in interstellar space the distance between two electrons is about 0.55 CIn The electric force between the two clectrons 38 1 repulsive 2.attractive. 017 (part 2 of 2) 10.0 points Calculate the electric force betwecn these two electIOns. The value of the Coul...

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