252x0313 9 26 03 ECO252 QBA2 FIRST HOUR EXAM October 2 2003 Name Hour of class registered Show your work Make Diagrams I 8 points Do all the following Normal distribution problems 1 The owner of a fish market determined that the average weight for a catfish is 3 2 pounds with a standard deviation of 0 8 pounds Assuming the weights of catfish are normally distributed the probability that a randomly selected catfish will weigh more than 4 4 pounds is 2 The owner of a fish market determined that the average weight for a catfish is 3 2 pounds with a standard deviation of 0 8 pounds Assuming the weights of catfish are normally distributed the probability that a randomly selected catfish will weigh between 3 and 5 pounds is 3 The owner of a fish market determined that the average weight for a catfish is 3 2 pounds with a standard deviation of 0 8 pounds A citation catfish should be one of the top 2 in weight Assuming the weights of catfish are normally distributed at what weight in pounds should the citation designation be established Find x 02 4 The owner of a fish market determined that the average weight for a catfish is 3 2 pounds with a standard deviation of 0 8 pounds Assuming the weights of catfish are normally distributed the probability that a randomly selected catfish will weigh less than 2 2 pounds is 252x0313 9 26 03 II 5 points 2 point penalty for not trying part a A random sample is taken of the number of automobiles involved in fog related accidents on the New Jersey Turnpike The following data is found Accident 1 2 3 4 5 No of cars 30 3 2 5 4 a Compute the sample standard deviation s of the number of vehicles involved Show your work 3 b A turnpike spokesperson says that the mean number of automobiles involved in this type of pile up is at most 6 6 Use the mean and standard deviation that you computed above to evaluate this statement at the 95 confidence level 3 c Extra credit A turnpike spokesperson says that the median number of automobiles in one of these accidents lies between 3 and 5 Treating this as a confidence interval for the median what is the confidence level What about these data makes me suspect that locating the median is a better idea than the hypothesis test in b 3 2 252x0313 9 26 03 III Do all of the following Problems 17 points Show your work except in multiple choice questions 1 The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact car owners who would have purchased a passenger side inflatable air bag if it had been available for an additional cost of 300 The manager believes from previous information that the proportion is 0 30 Suppose that a survey of 200 new compact car owners is selected and 79 indicate that they would have purchased the inflatable air bag If you were to conduct a test to determine whether there is evidence that the proportion is different from 0 30 and decided not to reject the null hypothesis what conclusion could you draw 2 a There is sufficient evidence that the proportion is 0 30 b There is not sufficient evidence that the proportion is 0 30 c There is sufficient evidence that the proportion is not 0 30 d There is not sufficient evidence that the proportion is not 0 30 2 An entrepreneur is considering the purchase of a coin operated laundry The present owner claims that over the past 5 years the average daily revenue was 675 with a population standard deviation of 75 A sample of 30 days reveals a daily average revenue of 625 If you were to test the null hypothesis that the daily average revenue was 675 which test would you use 1 a z test of a population mean b z test of a population proportion c t test of a population mean d 2 test of population variance 3 How many Kleenex should the Kimberly Clark Corporation package of tissues contain Researchers determined that 60 tissues is the average number of tissues used during a cold Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold X 52 s 22 Suppose the alternative we wanted to test was H1 60 State the correct rejection region for 0 05 2 a Reject H0 if t 1 660 b Reject H0 if t 1 660 c Reject H0 if t 1 984 or t 1 984 d Reject H0 if t 1 984 4 ASW The average monthly income of recent WCU business graduates four years ago was 3200 I believe that the recent recession has lowered the income and think I have the data to prove it The data consists of 72 responses from a random sample of more recent graduates Find the correct set of hypotheses below 2 a H 0 3200 H 1 3200 b H 0 3200 H 1 3200 3 c H 0 3200 H 1 3200 d H 0 3200 H 1 3200 4 252x0313 9 26 03 5 Bassett et al p126 The manager of a bottling plant is anxious to reduce the variability of the weights of bottled fruit Over the last two years the standard deviation has held at 15 2 grams and the distribution of the weights is believed to be normal A new machine is introduced and the weights of the bottles in a randomly selected sample are 987 966 955 977 981 967 975 980 953 972 so that n 10 x 9713 and x 2 9435347 Does the new machine have better performance a State your null and alternative hypotheses 1 b Do a test of your null hypothesis using a test ratio and a 5 confidence level 3 c Do a 95 2 sided confidence interval for the parameter of interest 2 6 Bassett et al p121 A box of bolts comes from a manufacturer whose bolts supposedly have a mean length of 5cm and a variance of not a standard deviation of 0 05 A random sample of 10 bolts is taken with the following results 5 68 5 13 5 82 5 71 5 36 5 52 5 29 5 77 5 45 5 39 From these we calculate a sample mean of 5 512 We assume that the reported variance is a valid population variance and do not calculate a sample variance and we use a 5 significance level a Calculate a confidence interval for the mean on the assumption that the underlying distribution is normal Is the population mean significantly different from 5cm 2 b If instead we found x 5 0707 find a p value for the test 2 c If in b we found that these 10 bolts had come from a population of 50 how would this affect the p value You do not need to do any new computations but I expect a short understandable …
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