#6 Hypothesis Testing Name___________________________________ 1. In hypothesis testing, a type I error is a. failing to reject the null hypothesis when it is false. b. failing to reject the null hypothesis when it is true. c. rejecting the null hypothesis when it is true. d. rejecting the null hypothesis when it is false. 2. Given the alternative hypothesis that a new process is better than the old one, the Type I Error is to conclude that: a. the old process is as good or better when it is not b. the old process is better when it is c. the new process is better when it is not d. the new process is as good or better when it is 3. If the number of observations (n) is increased to 2n, the level of significance (ALPHA) is: a. increased b. unaffected c. decreased 4. The level of significance is (check all that apply): A. the probability of rejecting the null hypothesis when the null hypothesis is true. B. the magnitude of the sample size. C. symbolized by the greek letter ALPHA. D. none of the above. 5. True or False? If False, correct it: Level of confidence is another name for level of significance. 6. A result was said to be statistically significant at the 5% level. This means: a. the null hypothesis is probably wrong b. the result would be unexpected if the null hypothesis were true c. the null hypothesis is probably true d. none of the above. 7. If the P-value for your test statistic satisfies P > .25, then: (a) you would not reject H(O) (b) you would reject H(O) for ALPHA = .05 (c) you would reject H(O) for ALPHA = .10 (d) your acceptance region has a lower limit of .25 (e) none of these 8. In hypothesis testing, what is the function of a critical value that is taken from the tables? a. It is equal to the calculated statistic from the observed data. b. It is the point where the decision changes from reject to fail to reject. c. It is the center of the distribution of X's. d. It is a point which is 1 standard deviation away from the mean. 9. True or False? If False, correct it. If we would reject a null hypothesis at the 5% level, we would also reject it at the 1% level. 10. True or False? If False, correct it. One can never prove the truth of a statistical (null) hypothesis. One can only tend to discount it. 1 PRESENT YOUR WORK USING THE 6-STEP TEMPLATE FOR ALL PROBLEMS. I HAVE PROVIDED AN EXAMPLE HERE. 11. The Build-It-Yourself Company sells an unassembled desk at a super low price. Customers have complained that one of the desk shelves are not cut to the proper length, meaning the desk cannot be assembled properly. The desk shelf is specified to be 8 inches. The company takes a sample of 50 desk shelves and finds the average length to be 7.8 inches, with a standard deviation of 0.5. At a significance level of = 0.01, test to determine if these sample data support customer complaints. Step 1: Hypothesis statement: Step 2: Drawing Step 3: Determination of the Critical Statistic Step 4: Determination of the Test Statistic and p-value. (You will have to use an online calculator or web applet to determine the p-value) Step 5: Comparisons of statistics and probabilities, and Statistical Decisions about Ho. Step 6: Conclusion. 2 12. An insurance company suspects that the typical number of claims per major city is exceeding the past average of 70 claims, with standard deviation of 8.9. Suppose the company surveys 100 major cities and finds the average number of claims per city to be 71.8. At a significance level of = 0.05, test to determine if these sample data support the company's suspicion. 3 13. A local airport has modified its operations to help airlines reduce delays. Airport managers believe that these modifications have reduced the daily number of late departures. Typically, the average number of late departures on a given weekday is distributed normally with a mean of 46. The airport informally records the number of late departures for 12 weekdays and finds and average of 41 late departures per day, with a sample standard deviation of 11.9. At a significance level of = 0.05, test to determine if these sample data support managers claims of success. 4 14. A bottled water filling machine, when in perfect adjustment, fills the bottles with 12 ounces of water. A random sample of 25 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces, with a standard deviation of 0.24 ounces. With a 0.05 level of significance, test to see if the machine is in perfect adjustment. 5