252gras1 06 9 26 06 ECO 252 Second Graded Assignment R E Bove Name 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 x 3 vi x 3 vii x 3 viii x 3 ix s 5 x p 5 xi 3 xii 3 xiii p 5 Problem 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 mean e 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 Using the 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 x 65 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 showing whether it contradicts the null hypothesis b Use the data in problem 3 to test the hypothesis 50 252gras1 06 9 26 06 c 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 n x noes in column 1 Uncheck summarized data and let Minitab know that the data are in column 1 C1 Other options are unchanged
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