STA 6166 – Exam 1 – Fall 2011 PRINT Name ___________________________Q.1. An engineer is interested in the distribution of lifetimes (hours to failure) of computer monitors that her firm manufacturers. After sampling 50 monitors, observing their hours to failure, she observes a mean of 600 and a standard deviation of 120. These are the population mean () and standard deviation () for her firm’s manufacturing process. TRUE or FALSEQ.2. A plant researcher has measured the amount of growth among five plants that received a growth formula. He finds that the amounts of growth (cm) were: 40, 36, 24, 30, 20. p.2.a. Give the sample mean, median, and standard deviation of the amounts of growth (show all work).Mean = _______________ Median = _________________ Std. Deviation = __________________p.2.a. Give the mean and standard deviation in inches (1 inch = 2.54 cm 1 cm = ½.54 = 0.39 in)Mean = ________________ Std. Deviation = ___________________________Q.3. A magazine publisher includes winning coupons for an advertised product in 1% ( = 0.01) of the October issues of the magazine. A national firm buys a random sample of n=500 of the issues (assume the total number of issues is many times > 500). Let Y be the number of winning coupons the firm receives. Give the expected value of Y, and the probabilitythat they get 1 or fewer winning coupons. p.3.a. E(Y) = _________________________________________________________________________p.3.b. P(Y ≤ 1) = _______________________________________________________________________Q.4. Two reviewers (Rev1 and Rev2) are compared by their positive and negative reviews of 1000 movies:p.4.a. What is the probability both reviewers give the same review? _____________________p.4.b. What is the probability Reviewer 2 was positive, given Reviewer 1 was negative? __________________Q.5. A forensic researcher samples 100 adult males and 100 adult females and measures each subject’s right foot length (cm). The following table gives the summary results:p.5.a. Test H0: F = M (F - M = 0) versus HA: F ≠ M (F - M ≠ 0) at the significance level.p.5.a.i. Test Statistic: Answer ______________________________p.5.a.ii. Rejection Region: ___________________________p.5.a.iii. Conclusion (circle best answer):Conclude F > M Conclude F < M Do not reject H0: F = Mp.5.b.Compute a 95% Confidence Interval for F - M Answer ______________________________Q.6. A scientist wishes to estimate the mean length of wood boards with advertised length of 72” within 0.2” with 95% confidence. Based on a small pilot study, she believes the standard deviation is approximately 2” in individual boards. How many boards should she measure?Answer ______________________________Q.7. Heights of adult males (cm) are approximately normally distributed with M = 167 and M = 6. Heights of adultfemales (cm) are approximately normally distributed with F = 160 and M = 5. p.7.a. What proportion of males are taller than 175 cm?Answer ______________________________p.7.b. What is the 95th %-ile among female heights?Answer __________________________________Q.8. In a population of people on a “Singles Cruise”, 60% are females and 40% are males. Among the females, 20% areactually married (and cheating on their spouse), among males, 40% are married.p.8.a. What is the probability a randomly selected “single” is actually married?Answer _________________________________________p.8.b. Given the randomly selected “single” is married, what is the probability that it is male?Answer _____________________________________________Q.9. Random samples of 5 inter-arrival times of volcano eruptions are obtained for each of 2 volcanoes in South Americaand are given in the following table.p.9.a. Assign ranks to the 10 inter-arrival times (Y, in years), where 1 is the smallest and 10 is the largest. p.9.c. The rejection region for a 2-sided Wilcoxon Rank-Sum test ( = 0.05) that the population means (medians) areequal is (for n1 = n2 = 5): Reject H0 if min(T1,T2) ≤ 17. Can we conclude the true means (medians) differ for thesevolcanoes? Yes / NoQ.10. An author wishes to demonstrate that the average number of typographical errors per page in his (very long) book isless than 1 per page. He wishes to test H0: = 1 HA: < 1 at = 0.05 significance level.Assuming the standard deviation is 0.9, how many pages will need to be sampled to have power = 1- = 0.80 when in factthe true mean is = 0.7Answer ______________________________p.9.b. Compute the rank sums for each volcano.p.9.b.i. T1 = _____________________________p.9.b.ii. T2 =
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