252x0753 9 26 07 Open in Print Layout format ECO252 QBA2 Name FIRST EXAM Class hour October 4 and 8 2007 Version 3 Student number Show your work Make Diagrams Include a vertical line in the middle Exam is normed on 50 points Answers without reasons are not usually acceptable I 8 points Do all the following x N 4 11 1 P x 0 2 P 33 x 2 3 P 4 x 4 4 x 075 Do not try to use the t table to get this 1 252x0753 9 26 07 Open in Print Layout format II 9 points 2 point penalty for not trying part a Monthly incomes in thousands of 6 randomly picked individuals in the little town of Rough Corners are shown below 2 5 7 3 3 1 2 6 2 4 3 0 a Compute the sample standard deviation s of expenditures Show your work 2 b Assuming that the underlying distribution is Normal compute a 99 confidence interval for the mean 2 c Redo b when you find out that there were only 50 people living in Rough Corners 2 d Assume that the population standard deviation is 2 and create an 85 two sided confidence interval for the mean 2 e Use your results in a to test the hypothesis that the mean income is above 2 3 thousand at the 99 level 3 State your hypotheses clearly f Extra Credit Given the data test the hypothesis that the population standard deviation is below 2 3 2 252x0753 9 26 07 Open in Print Layout format III Do as many of the following problems as you can 2 points each unless marked otherwise adding to 13 points Show your work except in multiple choice questions Actually it doesn t hurt there either If the answer is None of the above put in the correct answer if possible 1 If I want to test to see if the mean of hypothesis is i 0 x is smaller than the given population mean 0 my null ii 0 iii 0 iv 0 v Could be any of the above We need more information vi None of the above 2 Assuming that you have a sample mean of 100 based on a sample of 36 taken from a population of 300 with a sample standard deviation of 80 the 99 confidence interval for the population mean is 80 a 100 2 576 36 b 100 2 576 c 100 2 576 300 36 80 300 1 36 80 300 d 100 2 724 80 e 100 2 724 300 36 80 300 1 36 300 80 f 100 2 724 36 g 100 2 438 80 300 h 100 2 438 300 36 80 300 1 36 80 i 100 2 438 36 j 100 2 438 300 36 300 1 80 300 g None of the above Fill in a correct answer 3 252x0753 9 26 07 Open in Print Layout format 3 Which of the following is a Type 2 error a Rejecting the null hypothesis when the null hypothesis is true b Not rejecting the null hypothesis when the null hypothesis is true c Not rejecting the null hypothesis when the null hypothesis is false d Rejecting the null hypothesis when the null hypothesis is false e All of the above f None of the above 4 If a random sample is gathered to get information about a population proportion what do we mean by a p value a P value is the probability that if the null hypothesis was false that if we were to repeat the experiment many times we would get a sample proportion as extreme as or more extreme than the sample proportion actually observed b P value is the probability that if the null hypothesis was true that if we were to repeat the experiment many times we would get a sample proportion as extreme as or more extreme than the sample proportion actually observed c P value is the population proportion in the null hypothesis d P value is the population proportion in the alternate hypothesis e P value is the probability of a type 2 error f P value is the probability that the alternate hypothesis is true given the sample proportion actually observed g None of the above is true 5 If a difference in proportions in a business related problem is called statistically significant at the 1 significance level this means that a If the null hypothesis is true the difference in proportions is surprisingly large b There is a 99 chance that the null hypothesis is true c The difference in proportions is large enough so that we must take account of it in our business decisions d All of the above 6 Wonnacott Wonnacott When an industrial process is in control it produces bolts with a hardness that has a mean of at least 80 and a population standard deviation of 8 If the hardness is too far below 80 you must shut down the process Every hour you take a sample of 16 bolts How low must the average hardness of these bolts be before we shut the process down Use a 10 significance level and don t forget to state your hypotheses 3 7 Your boss who doesn t know any statistics tells you to shut down the process in 6 if the hardness level from a sample of 16 bolts is 79 or lower It is known that the population standard deviation is 8 If we assume that the process is producing bolts with an average hardness of 80 what is the probability that it will be shut down Think p value 2 15 4 252x0753 9 26 07 Open in Print Layout format 8 A 1989 Gallup poll revealed that 59 of women believed that the Republican Party were more likely than the Democratic Party to keep the country prosperous My how things change We were already sure that 68 of men believed that this was true a How many women had to be polled before we could state that the proportion for women is 59 03 Use a 5 significance level 2 b If we wished to test our belief that women were less likely to believe that the Republicans were more likely than the Democratic Party to keep the country prosperous and we were already sure that 68 of men believed that this was true let p represent the proportion of women What are our null and alternative hypotheses 1 c The actual poll covered a sample of 750 women Using a 95 confidence level and assuming that your hypothesis in b is correct test the hypothesis 2 20 5 252x0753 9 26 07 Open in Print Layout format Blank page for calculations 6 252x0753 9 26 07 Open in Print Layout format ECO252 QBA2 FIRST EXAM October 8 2007 TAKE 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 you do helps and grades wrap around Show your work State H 0 and …
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