252gras1-06 9/26/06ECO 252 Second Graded AssignmentR. E. BoveName: Class days and time:Student Number:Please include class and student number on what you hand in! Papers should be stapled. Your writeup should state clearly what you did and concluded.Problem 1: Which of the following could be a null hypothesis? Which could be an alternative hypothesis? Which could be neither? Why?(i)3, (ii)3, (iii)3, (iv)3, (v)3x, (vi)3x, (vii)3x, (viii)3x, (ix)5s, (x)5p, (xi)3, (xii)3,(xiii).5.pProblem 2: A man walks into a bar. He drinks 15 bottles of beer. These bottles are supposed to contain 12 ounces of beer with a population standard deviation of 0.2 ounces. On the basis of the man's condition when he leaves the bar, we conclude that the sample mean for the bottles was 11.80 ounces. Test the hypothesis that the population mean for these bottles was 12 ounces. Assume that the confidence level is 95%.a) State your null and alternative hypotheses.b) Find critical values for the sample mean and test the hypothesis.c) Find a confidence interval for the sample mean and test the hypothesis.d) Use a test ratio for a test of the sample meane) Find a p-value for the null hypothesis using the Normal table and use the p-value to test the hypothesis. Problem 3: A psychiatrist is treating a group of aborigines who are suffering from depression. Whether justifiably or not, she considers this group a random sample of 15 taken from a very large number of depressed individuals. The numbers below represent the measurement of the sample’s level of depression an hour after taking the pill using a commonly used (Coolidge Axis II) scale for measuring depression. Personalize the data as follows: add the digits of your student number to the last six numbers. Example: Ima Badrisk has the student number 123456; so the last six numbers become {51, 52, 53, 54, 55, 56}. 52 53 58 50 53 58 55 66 53 50 50 50 50 50 50 Compute the sample standard deviation using the computational formula. (If you did this correctly on the last assignment, just copy your work.) The doctor believes that subjects fed a sugar pill will have an average score on the same scale of 58.73. a) Test the validity of the doctor’s hypothesis using a confidence level of 95% and a critical value for the sample mean. (You cannot test the validity of a hypothesis that you haven’t stated!)b) Find an approximate p-value for the statement.c) Will we reject the doctor’s hypothesis at a confidence level of (i) .001? (ii) .01? (iii) .10? Usingthe p-value explain why. Note that none of the problems beyond this point involve sample means.Problem 4 (Moore): 40% of Americans claim that they attend church weekly. You believe that the proportion is below 40%. Your henchpersons follow around a random sample of 200 people for a week. They find that x people attend church. (To calculate the number x, add the 2nd to last digit of your student number to 60. If the second to last digit of your student number is 0, add 10. Example: Ima Badrisk has the student number 123456; so she says that 65x.)a) State your null and alternative hypotheses.b) Find a test ratio for a test of the proportion.c) Find a p-value for this ratio and use it to test the hypothesis at a 5% significance level.Extra Credit Problem 5: a) Finish problem 4 by finding an appropriate confidence interval for the proportion and showingwhether it contradicts the null hypothesis. b) Use the data in problem 3 to test the hypothesis .50252gras1-06 9/26/06c) Use Minitab to check your answer to problem 4. Do this three ways First: Enter Minitab. Use the Editor pull-down menu to enable commands. Then enter the commands below. Pone 200 x; (Replace x with the number you used.) Test 0.4;Alter -1; (Makes H1 ‘less than.’)useZ. (Uses normal approx. to binomial)Second: Use the Stat pull-down menu. Choose ‘Basic Stat’ and then ‘1 proportion.’Check ‘summarized data’ and enter your n and x. Press Options. Set ‘test proportion’ as 0.4, alternative hypothesis as ‘less than’ and check ‘Normal distribution.’ Go.Third: Use the pull-down menu again. But before you start put x yeses and xn noes in column 1. Uncheck ‘summarized data’ and let Minitab know that the data are in column 1 (C1). Other options are
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