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Part 3: Perform each hypothesis test: Show all steps to each hypothesis test!A national magazine claims that the average amount of time that people watch &x per...

Question

Part 3: Perform each hypothesis test: Show all steps to each hypothesis test!A national magazine claims that the average amount of time that people watch &x per week is 25.2 hours per week sample of 30 college students has an average of 24.8 hours With standard deviation of 3.5 hours_ At a 10%0 significance level can we conclude that college students watch less tx? (Use the Critical Value Approach ) points)

Part 3: Perform each hypothesis test: Show all steps to each hypothesis test! A national magazine claims that the average amount of time that people watch &x per week is 25.2 hours per week sample of 30 college students has an average of 24.8 hours With standard deviation of 3.5 hours_ At a 10%0 significance level can we conclude that college students watch less tx? (Use the Critical Value Approach ) points)



Answers

Instructions: For the following ten exercises, Hypothesis testing: For the following ten exercises, answer each question.
a. State the null and alternate hypothesis.
b. State the p-value.
c. State alpha.
d. What is your decision?
e. Write a conclusion.
f. Answer any other questions asked in the problem.
The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of 30 freshman students and found a mean study time of 137 minutes with a standard deviation of 45 minutes. At ? = 0.01 level, is the student academic group’s claim correct?

All right for this question they are asking us to find first the null hypothesis in the alternative hypothesis is so we have a claim that the freshman students on a campus study at least 2.5 hours per day. The null hypothesis is that claim so freshman study at least greater than equal to 2.5 hours for a day. And the alternative hypothesis is what the statistics cost. They're skeptical of this claim. So the alternative hypothesis is that freshman studied less than 2.5 hours per day. So what we need to do is we need to figure out is this null hypothesis Is this claim true? In order to do that, we need to find the p value. So in order to find the P value, the first thing we need to do is find the test statistic on that shows us how many standard deviations away from the mean is the results. So our T statistic, we find that with the formula of the, um, sample me and minus the population mean over the sample standard deviation over the square root of the sample size. So when we put that information in, Um, we're gonna go ahead and convert the minutes in the problem. Two hours. Um, to do that, you just divide by 60. So we have our 137 minutes becomes too point to a hours minus 2.5 hours over the sample standard deviation, which is, um, 0.75 hours, 45 minutes. It's 450.75 hours divided by the square root of the sample size, which is 30. And when you put that in your calculator, you get negative 1.6 07 Now that we have our t score, um, we need to find the P value. To do that, all you need to do is look up a tea table. You can even just google that and you'll find a tea table. You find negative 1.6 of seven, and it will give you the P value. The P value that you are given with that, um, to score is 0.6 now. What this means is that the probability of getting 137 minutes as the means so that's the 2.28 hours in the study is basically a 6% chance if the null hypothesis is true. So in order to decide about this study, we need to know what Alfa is. Alfa is the significance level. So Alfa is the probability of rejecting the null hypothesis when in fact it's actually true. The Alfa that they gave us is 0.1 which means that 1% of the time on the threshold is 1% of the time. You would reject the normal hypothesis when, actually it's true. Our P value, as we've already found, is 0.6 If the P value is higher than the Alfa, then that means that we do not reject the NOL. We keep the null. So go ahead and write for our d um, that we failed to rejection and all the P value. When the pea value is high, then all flies. When the people you is low, the norm must go. So that's a little saying to help you remember. So since the P value is greater than Alfa, then re failed to reject. So our conclusion in summary is that the student claim that freshman study at least two enough hours today is correct hours per day, and what it means is that we at least it's true. Um, what it means is that at least we don't have enough evidence to say that that's not true. So we're going to say that, according to this study, that the null hypothesis we cannot reject it, that it is still true that freshman students study at least 2.5 hours pretty.

The variable is tv viewing time. The two populations are married men and married women. The testing population or identifying the pears are married couples were trying to find the difference between the tv viewing times of a married couple. If we let U. One and U. Two. To note that mean, tv viewing times of married men and women, respectively. This means that for the null hypothesis, me one is equal to meWTwo. And if we let men the new one, we hypothesize that men watch less tv. So it's me one is less than you two, which means that we are doing a left tail test.

So we have a high set of hypotheses that we need to write down. We're going to assume that the mean cost of the braces is the $5400 and alternately they think that they're actually less than that. And so we are dealing with a sample of size and put that information here size 28 and they get an X bar that is $5250 and a standard deviation from that sample that is 629. And we are supposed to use an Alfa level for our decision of 0.252 point 5%. So we want to look at what the critical, uh, t value is. This is going to be a T distribution, and the critical T value is going to be a value down here. We want this to be 0.25 We want to find the t value that corresponds with that that has 27 degrees of freedom. And if we look that up in our table, we know it's going to end up being negative. We actually look up the value over here, and when I look at row 27 go 2.25 in the upper tail. It gives me 2.52 So are critical. T value will be 2.52 But negative. Since we're down in this lower end and then on part C, we want to find what the test statistic is going to be, and it's going to be a t value. It's gonna be a T value. That is what we got, which is 5250 minus what we're assuming 5400 over the standard deviation or the square root of n. And when I got sought, this difference here is negative 1 50 divided it by and just double check on my calculator. I get that that test statistic is equal to negative 1.26 And so we can see that, according to our next part, asked us on part D to determine let's see, to determine. Yeah, looking for the actual textbook here Looks like we're determining with our steps. Part D is to make a decision, and so on part d. We know our test statistic is way over here, so we do not have evidence to reject the null. So since our test statistic is not down below here we we have no evidence or we fail. We'll say it that way. We fail to reject and all. So our conclusion would be that the mean amount does seem to be mean. Does seem to be $5400. We don't have evidence to say it's lower. Um, now I don't usually find the critical t value. I usually set it up like this. I usually take the problem. And I know 5400 is what we're assuming and what we got was 5000, 250 I find this area, which is R P value. And so we would find what's the probability of getting a mean of less than or equal to 5250. And that corresponds with converting it to the test statistic with 27 degrees of freedom to that negative 1.26 and then finding the P value which I can actually do with my calculator. Doing that second distribution and doing uh huh. Finding my t distribution here. Uh, Denver, uh, the TCD app and the TCD up putting in negative large number negative 1000 would be fine And then using the upper of negative 1.26 Oh, and our degrees of freedom is 27 and then just have a little air here. Yeah, let's see. Here we go and I get my P value is 0.1092 And so this by far is not less than this. 2.5%. So again, we would have would not have evidence to, uh, to reject the null. We would fail to reject the null and say we believe that the alternative is actually true. So you have a couple of different ways you can set it up. I prefer this by myself because I like to find out what that P value is.

Everyone said they were gonna be looking at her, but sees that we use for hypothesis. Tests have been given four different scenarios to work with. So the first scenario we're looking at the age of enrollment for evening classes at a certain college, and the question is suggesting that the mean age is greater than 26 years. And so for that we could see that the alternative hypothesis is being suggested is that it's great from 26 which means the null hypothesis is that the mean age is actually equals 26 which is equivalent to saying it's the last tunnel equal. And I'll send if coupled. Cysts sent me is Oh, sorry, you is greater than 26. And so we did this by identifying in the question that the thing that is being suggested, the alternate to the normal that's being suggested is that the ages great on 26 on the alternative to this or the status quo is that we were assumed that the age is 26 or that it's less than or equal to 26. So very similarly, we're gonna move on to the next part, which is asking about the weight of packages that are being shipped and it suggesting that the mean weight was less than £36.7. And so, ah, no hypothesis, because this question is suggesting that hypothesis in which the mean, where is less than 36.7 to say that the mean is equal to 36.7 or greater than or equal to. That's because alternative I bought says is that the mean weight is actually less than 36.7. We used this symbol here. Teoh sort of demonstrate that all the whole range of values is covered with not forgotten about the values greater than a story about 36.7. So party is talking about the life off light bulbs on it, suggesting that the mean life is less is at least 16 100 hours. And they wanted to. At least we're talking that it's greater or greater than or equal to 1600 hours. So that means that we're suggesting that the for occasional what suggesting that the main is equal to, uh, 1599 because we want the alternative to be that it is great to them. 15 years that it is at least 1600. So you weren't here century quilting and for d again a very simple process. Looking at the strength off welds, Um, in suggesting that means drink by using a new process is different from the old process, which had a strength of £570 per unit area. So that means that the whole process the no or the the normal way of things is that the main is equal to 570 on this alternative hypothesis it's being suggested is that new is in fact, uh, different from this but that we write this sign, which just means is not equal. Teoh 517 two days of the hypotheses that would suggest for these questions. And it's really about deducing what the question means on what it's talking about.


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