252x0313 9/26/03 ECO252 QBA2 Name ___________________ FIRST HOUR EXAM Hour of class registered _____ October 2, 2003Show 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 02.x)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 No. of cars 1 30 2 3 3 2 4 5 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)2252x0313 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 meanb)z-test of a population proportionc)t-test of a population meand)2-test of population variance3. 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 wasH1: 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)3200:3200:10HHb) 3200:3200:10HH3c) 3200:3200:10HHd)3200:3200:10HH4252x0313 9/26/035. (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 andthe 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 972,953,980,975,967,981,977,955,966,987, so that ,10n9713x and 94353472x. 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:39.5,45.5,77.5,29.5,52.5,36.5,71.5,82.5,13.5,68.5. 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 0707.5xfind a p-value for the test . (2)c) If in b, we found that these 10 bolts had come from a population of
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