Download Statistical Hypothesis Testing and Regression Analysis - Prof. B. Bare and more Exams Probability and Statistics in PDF only on Docsity! Final Examination Q SCI 381 Dr. Bare Name: ________________________ Final Examination Closed book. May use calculator and formula card. Show all work for full credit. This means show which formula is used; plug in a few representative data points to demonstrate that you know how to use the formula; provide the correct numerical answer. (200 points) (25) 1. A physician claims that adult Americans who smoke more than two packs of cigarettes per day weigh less than the average weight of all American adults. A random sample of 25 two pack a day smokers has a mean of 140.6 lbs. and a standard deviation of 5 lbs. The weight of all adult Americans is approximately normally distributed. If the average weight of all adult Americans is 145 lbs., is there enough evidence to support the claim at =.01? a) Provide a mathematical description of the null and alternative hypotheses. b) Calculate the test statistic. c) Find the critical value (s). d) Make a decision. e) State your conclusion in words. Final Examination (25) 2. A local brewery claims that the variance of the sugar content of its India Pale Ale (IPA) is less than or equal to 10 milligrams per 12 ounces. A random sample of 16, 12- ounce bottles is selected and the sugar content is measured. Sugar content of IPA is approximately normally distributed. The variance of the sample is found to be 20 mg. At = .05, is there enough evidence to reject the claim? a) Provide a mathematical description of the null and alternative hypotheses. b) Calculate the test statistic. c) Find the critical value (s). d) Make a decision. e) State your conclusion in words. f) Give the range for the approximate P-value for this test. 2 Final Examination (25) 5. A local polling company claims that 85% of the adult American population opposes replacing $1 bills with $1 coins. To test this claim, we take a random sample of 120 American adults and find that 110 are opposed to replacing the $1 bills. At =.01, do we have sufficient evidence to refute the claim? a) Provide a mathematical description of the null and alternative hypotheses. b) Calculate the test statistic. c) Find the critical value (s). d) Make a decision. e) State your conclusion in words. f) Determine the approximate P-value. 5 Final Examination (15) 6. Using the same data from the previous problem, a) What is the maximum error of estimate of the adult American population that opposes replacing $1 bills with $1 coins? Recall that =.01, n=120, and x=110. b) What sample size is required if we wish our maximum error of estimate to be 4%? (10) 7. If 2% of all eastern Washington August wild fires burn in excess of 5,000 acres, find the probability that in a random sample of 100 fires, 4 will burn I excess of 5,000 acres. (15) 8. The miles per gallon for 10 randomly selected 4-wheel drive SUVs in city driving are shown below: 12 18 15 16 16 14 12 15 16 17 a) Construct a frequency distribution with three classes such that the mid-point of the first class is 13. b) What is the class width? c) What are the class boundaries of the second class? d) If the data were presented to you in the form of the frequency distribution developed in part (a), what would be your estimate of the mean miles per gallon? 6 Final Examination (25) 9. A medical researcher wishes to see whether the variances of the heart rates (beats/ minute) of smokers are different from the variances of heart rates of people who do not smoke. Heart rate is approximately normally distributed. Two independent random samples are selected with the following results. At =.05 is there enough evidence to support the claim? Smokers Non-smokers n1 = 32 n2 = 28 s12 = 34 s22 = 15 a) Provide a mathematical description of the null and alternative hypotheses. b) Calculate the test statistic. c) Find the critical value (s). d) Make a decision. e) State your conclusion in words. 7
