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. 11,4~ Nx1. 0xP2. 233 xP3. 44 xP4. 075.x (Do not try to use the t table to get this.)1252x0753 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 3.0a. 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 themean. (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 below2. (3) 2252x0753 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 x is smaller than the given population mean 0 my null hypothesis is:i) 0 ii) 0 iii) 0 iv) 0 v) Could be any of the above. We need more information.vi) None of the above2) 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 a) 3680576.2100b) 3680130036300576.2100c) 30080576.2100d) 30080724.2100e) 3680130036300724.2100f) 3680724.2100g) 30080438.2100h) 3680130036300438.2100i) 3680438.2100j) 30080130036300438.2100g) None of the above. Fill in a correct answer.3252x0753 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 abovef) 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 theexperiment 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 thata) 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 above6) (Wonnacott & Wonnacott) When an industrial process is in control, it produces bolts with a hardness thathas a mean of at least 80 and a (population) standard deviation of 8. If the hardness is too far below 80, youmust shut down the process. Every hour you take a sample of 16 bolts. How low must the average hardnessof 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]4252x0753 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 is03.59. ? (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]5252x0753 9/26/07 (Open in ‘Print Layout’ format)Blank page for calculations 6252x0753 9/26/07 (Open in ‘Print Layout’ format) ECO252 QBA2 FIRST EXAMOctober 8, 2007TAKE HOME SECTION- Name: _________________________ Student Number
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