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ISuTbeahin beloorarr ine mumbenofcass,in thousands; produced by the brewery'$ day xd shift_-Thechif was operating normally throughouLthc_Wcck Monday 12.8 Tuesd...

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ISuTbeahin beloorarr ine mumbenofcass,in thousands; produced by the brewery'$ day xd shift_-Thechif was operating normally throughouLthc_Wcck Monday 12.8 Tuesday 13.2 Wednesday < 112 Thursday 12.5 Fnday' 14.3What is the avcrage number of cases the shill produced per day this week. 2 pls_ 3 Acan % n-nlbt & 61 IM sf' 8 PrducA ev 4as 4Al, we "$ 12 42 7 4 4 ~62P 64 =42. % What is the median numbcLoCcases the shif produced per dey lhis weck: 2 pts_ 42.5(12.8) ) 3 2 14.2 tk

iSuTbeahin beloorarr ine mumbenofcass,in thousands; produced by the brewery'$ day xd shift_-Thechif was operating normally throughouLthc_Wcck Monday 12.8 Tuesday 13.2 Wednesday < 112 Thursday 12.5 Fnday' 14.3 What is the avcrage number of cases the shill produced per day this week. 2 pls_ 3 Acan % n-nlbt & 61 IM sf' 8 PrducA ev 4as 4Al, we "$ 12 42 7 4 4 ~62P 64 =42. % What is the median numbcLoCcases the shif produced per dey lhis weck: 2 pts_ 42.5(12.8) ) 3 2 14.2 tk a d(1 d3im M a&an 2 12 What is the population standard deviation of the number ofcases the shif produced per day this weck 6 pts X 12



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A commercial farmer harvests his entire field of a vegetable crop at one time. Therefore, he would like to plant a variety of green beans that mature all at one time (small standard deviation between maturity times of individual plants). A seed company has developed a new hybrid strain of green beans that it believes to be better for the commercial farmer. The maturity time of the standard variety has an average of 50 days and a standard deviation of 2.1 days. A random sample of 30 plants of the new hybrid showed a standard deviation of 1.65 days. Does this sample show a significant lowering of the standard deviation at the 0.05 level of significance? Assume that maturity time is normally distributed. a. Solve using the $p$ -value approach. b. Solve using the classical approach.

So for 21 the first thing we have to do is find the mean and standard deviation. So if you put him in your calculator, run won their stats. You will find that the mean is 53 point A with a standard deviation of 3.42 So we want to know how many of our items are within one standard deviation, two standard deviations and three standard deviations. So if we add the standard deviation to are mean and subtract the standard deviation, that gives us a range. A 50.38 2 57 22. There are seven numbers in that range. Two standard deviations. So subtract another 3.42 and add another three point for two gives us 46.96 to 60.64 Nine items are in that range and then going out one more standard deviation. 43.54 2 64.6 includes all Ted

All right, so we're on question. Number 53 talking about a farmer's market. So farmer has £100 of apples, £50 of potatoes, and he's trying to take them thio the market to sell. Um, and so when you do that, there's a market price for Apple's that's determined by with an average, um and then same thing goes with the average sale for the pound of potatoes. And they're saying so let's go ahead and put in that information on here that the apples average is going to be a $0.5 or 50 cents. Um, and then the Senate deviation is equal $2.2 for potatoes. Its average is going to be a $0.3 and its sanity aviation is $0.1. Okay, so we have to keep in mind that there are £100 of apples and £50 of potatoes were letting a be the price of apple pounds P is the price of potato pounds. And it does say here that it is going to be a $2 cost thio, uh, to I think to transport cost him $2 to transport all the apples and potatoes to the market, meaning he's using up gas money and all that stuff to bring that to the markets. That's gonna be a minus two. So we define the variables. That's A and P, and we're gonna use him to express his income. So we have to keep in mind. Okay, so he's gonna have an income. If he sells all of this stuff, that would be 100 times a plus 50 times p and then minus the $2 that it takes for him to get there, that will be his income or his profit. Um And then in part B, we are asked to find the actual mean So that would involve us doing, ah 100 times the average cost. So $1000.5 plus 50 times its average mean is $0.3 and then subtract the $2 it cost to bring their. So if we do that now, that ends up being 50 plus 15 minus two, which is equal to $63 were then asked in part C to find the standard deviation of this net income. So we have to remember that standard deviation is a little bit different. We have to dio that squaring situation. So we're gonna have a big square root. We're gonna square root. Ah, 100 squared times the 0.2 squared plus always edition their 0.5 squared times the 50 squared. And so when we do that, we get 400 plus 25 which is 425 when we square root for 25 that's gonna be approximately $20.62 when we round it. So then part D. The last thing is asking us, Do you need to make any assumptions in calculating the mean? And what about the standard deviation? So the answer for the mean assumptions is, uh, no, we don't have to make any assumptions there, but with standard deviation, you do have to make sure that it's independent. You have to assume independence. All right,

We're told the population has mean new equals 8.8. And are given in the following sample data randomly selected from that population from that sample thing that we want to calculate the mean X bar and the sample standard deviation S. So to do so let's remember the formulas for each of these terms, sample mean X bar is defined as the sum of the data that I am in this case 7.36 And the sample standard deviation is defined as some of the deviation about the mean squared all divided by n minus one. In this case, 4.3 Next. What we want to do Is used the sample data to implement a two tailed test. That is we want to test whether or not the sample data suggests the actual meaning. The population differs from the nomen of 8.8 in either direction, higher or lower. We want to use significant level Alpha equals 0.5 And we note at this point that X. Is approximately normally distributed. So to answer this test question, we have to go through the following procedures in order to finalize The solution of this test. So first, what's the significance level? And hypotheses are physical. 0.05. No hypothesis H. Not musicals. 8.8. H. A mute does not equal the population. 8.8. What distribution are using completely associated test statistic? The distribution. We're going to use the student's T distribution because our population standard deviation sigma is unknown. We can definitely use this distribution though, because the shape is appropriate. Ak because X is approximately normally distributed, it's okay to use a student's T distribution. Next, what is the T stat stat is defined by this formula, which here we see, reduces down to T equals negative 1.337 Next let's use the T stat to compute the p and dribble and sketch this out on the student's T distribution. So since we have degree of freedom and minus one equals 13, we're going to use the two tailed T table, which you can find either on google and a staff textbook to identify what range of p values this T stat negative 1.337 falls between, we find it falls between 0.2 and 0.25 We can graph this as the area underneath the student's T distribution, which we highlighted here in yellow outside of our T stat. Uh In this case we have both negative 1.337 and positive 1.337 Because the detailed test next, what can we conclude from this? Well, he is greater than alba. So we have statistically insignificant findings, i. E. We cannot reject h not or no hypothesis. And that ultimately means that we lack evidence suggesting that the population mean differs from its no mean of a pointing

Look expert. A salary expenses, Judy five day would be Uh huh, the flyby. The salary experience. Let's bring this duty weekends. Given the mean and standard deviation values for X and Y and the standard deviation value says 1 29 and 57 will find a radiance ing Mosque away. That this 6 16,041 and 3000 2 49 No, we have to find a meeting Standard deviation office Total weekly salaries that will be for X and Y X place by so we'll find you've expressed by there is equal to your face lazy over I though there's 1000 to 50. Let's 4 50 That was 1007 100. No, we fight the Stein in division for experts. Wife Sigma X Plus y converted nuts squared off millions Morph Expressway. Since X plus X and Y are independent way have bearings off explains. Why is equal toe really interface less variant off? Why that is giving There is 6 15,041 flesh. 3000 2 49 It's 8 19,090 that is your little 1 41 point $03


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