GBS 221 Trollen Exam 3 NAME ___________ 1. [15 pts] Circle the best answer in the brackets. a) The probability of a Type I error is denoted by [ α | β | 1-α | 1-β ]. b) When a decision maker doesn’t reject the null hypothesis, she runs the risk of a Type [ α | I | II | p ] error. c) A researcher cites that the p−value for her sample result was .20. You prefer to perform hypothesis tests at the 5% level of significance. Applying your level of significance to her results, you [ can | cannot ] reject H0. d) When all of the values plotted on a control chart lie within the upper and lower control limits and exhibit random variation, we conclude that [ no | common cause | assignable cause | pooled ] variation was present. e) A(n) [ X-bar | R | np | p ] chart is used to track item variation over time. 2. [3 pts] Joe Zin’s financial advisor predicted his portfolio’s mean rate of return would be at least 12.1%. What are the appropriate hypotheses? H0: _______________________________________ HA: _______________________________________ 3. [4 pts] Consider the hypotheses: H0: The new plan is superior to the old plan HA: The new plan is inferior to the old plan a) Explain in terms of this scenario what a Type I error would be. b) Explain in terms of this scenario what a Type II error would be. 4. [4 pts] A researcher was testing H0: µ < 40 vs. HA: µ > 40. A summary of the results is given below. Unfortunately the p-value didn’t print. What is the p-value? TEST OF MU = 40.0 VS MU G.E. 40.0 N MEAN STDEV SE MEAN Z P VALUE C1 150 40.79 4.57 .373 2.12 ???? 5. [3 pts] When testing the difference between means, what is the advantage of using paired samples? 6. [3 pts] A large shipment actually contains 10% defective items. If the receiving organization’s acceptance sampling plan calls for n=20 and c=3, what is the probability that the shipment will be accepted? 7. [3 pts] A sample of 15 parts will be taken from a large shipment. Given that p0 and p1 each =.05, what acceptance number will limit the Producer’s risk to 10% or less?Use the worksheets to perform a hypothesis test for each of the next three problems. In step 6, state your conclusion in terms relevant to the scenario. 8. [18 pts] A study conducted 5 years ago revealed that 18 percent of adults wore seat belts. Since then, an alliance of government, insurance industry and civic leaders has coordinated a 5-year advertising blitz to promote seat belt usage. A survey has just been completed to determine whether the advertising has been effective. Of 2,000 adults polled, 604 indicated they regularly use seat belts. Can the alliance conclude that seat belt usage has increased? Test at the 3% level of significance. 9. [18 pts] Last year the mean expenditure for Christmas presents at Goldwadders department store was $37.50 per gift. Since the economy seems weaker this year, a retailer thinks the mean expenditure this year will be lower. To test her theory, a random sample of 25 Christmas expenditures was selected. The mean was $35.92 and the standard deviation was $4.00. Test the appropriate hypothesis at the 1% level. 10. [18 pts] Hurts Rent-A-Car will purchase new sub-compact cars to add to its fleet. Before making the final decision, management wants to determine whether there is any difference in the first-year maintenance & repair costs associated with the Chevy Nova and Toyota Corolla. For a random sample of 12 Novas, the mean first-year maintenance & repair costs was $43.22 with a standard deviation of $12.32. A random sample of 18 Corollas averaged $32.72 with a standard deviation of $8.32. What should management conclude at the 5% level. Assume the populations have equal variances. 11. [11 pts] BriteCo makes light bulbs. They periodically sample and test 20 newly-made bulbs to monitor the production process. You’ve been asked to prepare a control chart to monitor the proportion of defects. Sample 1 2 3 4 5 6 7 # of defectives 3 0 2 3 6 1 2 a) Calculate the centerline and control limits. b) Sketch the control chart. 1 2 3 4 5 6 7 c) Interpret the chart.b) p Chart results for the fraction of defectives in 20 samples: Center line at 0.12142857 Upper control limit at 0.34053504 Lower control limit at