252y061t 10/10/06 (Open in ‘Print Layout’ format) ECO252 QBA2 FIRST EXAMOctober 11-12 2006TAKE HOME SECTION- Name: _________________________ Student Number and class: _________________________ IV. Do at least 3 problems (at least 7 each) (or do sections adding to at least 20 points - Anything extra youdo helps, and grades wrap around) . Show your work! State 0H and 1H where appropriate. You have not done a hypothesis test unless you have stated your hypotheses, run the numbers and stated your conclusion.. (Use a 95% confidence level unless another level is specified.) Answers without reasons usually are not acceptable. Neatness and clarity of explanation are expected. This must be turned in when you take the in-class exam.1. (Moore, Notz) You are thinking that it may be desirable to start a wellness program for your (large) company. You are told that the company will only start such a program if you can show thatthe blood pressure of a group of mid-level executives is above normal. The individuals are all between 35 and 44 years old and US statistics show that mean systolic blood pressure for men in that age range is 128. You take a sample of 72 executives and get the following results.x 139.60 130.61 182.53 120.02 118.77 149.44 107.30 117.47 136.21 130.15 141.96 137.23 141.15 133.89 122.73 145.25 114.18 154.74 122.14 127.22 150.30 118.37 125.35 159.94 128.45 126.29 163.18 141.54 126.93 124.80 152.64 112.34 120.68 124.48 124.61 105.67 144.71 133.00 109.62 145.10 127.51 117.51 100.03 149.55 127.32 131.74 116.59 119.39 128.07 138.22 130.77 109.52 136.69 135.69 132.00 127.67 161.43 169.05 140.35 131.40 125.06 169.61 117.84 117.97 161.09 116.14 158.74 126.54 135.21 126.71 120.01 112.40To personalize the data below take the last digit of your student number, divide it by 10 and add it to the numbers below. If the last digit of your student number is zero, add 1.00. Label the problem ‘Version 1,’ ‘Version 2,’ … ‘Version 10’ according to the number that you used. (For example, Seymour Butz’s student number is 976502, so he will add 0.20 and change the data to 139.80, 130.81, 182.73 etc. – but see the hint below, you do not need to write down all the numbers that you are using, just your computations.) Hint - if you use the computational formula: For the original numbers ,72n 41.9528x and 7.12807632x. If you add a quantity a to a column of numbers, ,naxax 2222 naxaxax Assume that the Normal distribution applies to the data and use a 99% confidence level.a. Find the sample mean and sample standard deviation of the incomes in your data, showing your work. (1) (Your mean should be fairly near 132 and your sample standard deviationshould be near 16 or 17.)b. State your null and alternative hypotheses (1) c. Test the hypothesis using a test ratio (1) d. Test the hypothesis using a critical value for a sample mean. (1)e. Test the hypothesis using a confidence interval (1)f. Find an approximate p-value for the null hypothesis. (1)g. On the basis of your tests, will you get a wellness program? Why? (1)h. How do your conclusions change if the sample of 72 is taken from a population of 200? (2)i. Assume that the Normal distribution does not apply and, using your data, test that the median is above 128. (3) [12]j. (Extra credit) Use your data to get an approximate 90% 2-sided confidence interval for the median.252y061t 10/10/06 (Open in ‘Print Layout’ format)2. Once again, assume that the Normal distribution applies, but assume a population standard deviation of 16 and that we are testing whether the mean is above 128. (90% confidence level)a. State your null and alternative hypotheses(1)b. Find a p-value for the null hypothesis using the mean that you found in a. On the basis of your p-value, would you reject the null hypothesis? Why? (1)c. Create a power curve for the test. (6) [20]3. (Moore, Notz) A recent survey said that nationwide 73% of all freshman students identified being well-off financially as an important lifetime goal. You believe that the proportion of freshman business majors with that goal is higher than the national figure. You take a survey of a random sample of 200 students and find that a152 have being well-off as an important goal, wherea is the second to last digit of your student number. If the second to last digit of your student number is zero, 10a. (For example, Seymour Butz’s student number is 976502, so he will add 10 and say that 16210152 x.) Label your solution ‘Version a,’ where a is the number that you are using. a. Formulate your null and alternative hypotheses and do a hypothesis test with a 95% confidence level. (2)b. Find a p-value for the null hypothesis. (1)c. Find the p-value for the null hypothesis if ax 162 (1)c. (Extra credit) How would your answer to a) change if your sample of 200 came from a population of 300? (1)d. (Extra credit) Using a critical value of the proportion for testing your null hypothesis, create a power curve for the test by using the alternate hypothesis and finding the power for values of73.1p. (Up to 6 points)d. Assume that 73.p, how large a sample would you need to estimate the proportion above that have being well-off with an error of .005? (2)e. Use the proportion that you found in a) to create a 2-sided 95% confidence interval for the proportion. Does it differ significantly from .73? Why? (2) [28]4. Standard deviation is often a measure of reliability. A manufacturer is providing a connector with amean length of 2.5 mm and is getting complaints that the connector is often too large or too small for the intended use. The previous standard deviation to the length of the part was 0.025mm, but the manufacturer introduces a process that should make the standard deviation smaller. A sample of 25 items is taken which yields a sample standard deviation of a030.0 . To get a take the third to last digit of your student number and multiply it by 0.001. (For example, Seymour Butz’s student number is 976502, so he will subtract .005 and say that.025.0005.0030.0 s)a. Formulate the null and alternative hypotheses necessary to see if the goal has been achieved andtest the hypothesis using a 95%
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