Statistics 350 ? Homework #4 Name: ID Number: GSI Name: Lab Section Number: DUE: To your lab GSI at START of your lab session Feb 16-18. Print out these sheets two-sided. Write clearly in the spaces provided. Make sure you show all work. __________________________________________________________________________________________ 1. Assessing Response Bias: Many investigators have studied the effect of the wording of questions on surveys. Consider the following two versions of the same question concerning gun control Question A: Would you favor or oppose a law that would require a person to obtain a police permit before purchasing a gun? Question B: Would you favor or oppose a law that would require a person to obtain a police permit before purchasing a gun, or do you think such a law would interfere too much with a citizen?s right? Let pA = the proportion of all U.S. citizens who favor a police permit if they were asked Question A, whereas pB = the proportion of all U.S. citizens who favor a police permit if they were asked Question B. The researchers were interested in estimating the effect that the extra phrase in Question B (which reminds people about the right to bear arms) has on the proportion that respond in favor. a. The article ?Attitude Measurement and the Gun Control Paradox? (Public Opinion Quarterly, 1977-78, p427-38) reported the following results: Question A B Sample Size 615 585 Number in ?favor? 463 403 i. What proportion of those who were asked Question A responded in favor? _________________________ ii. What proportion of those who were asked Question B responded in favor? _________________________ b. Give an estimate of the difference in the population proportions pA ? pB. _______________________________ c. The researcher would like to use the results to create a 90% confidence interval for pA ? pB . i. Clearly state the necessary conditions and confirm that the conditions are met. ii. Create the 90% confidence interval estimate. Final answer: ( ___________ , ___________ ) d. The researcher speculates that the ?citizen?s rights? phrase in Question B will reduce the rate of those that respond in favor. Does your interval in part (c, ii) support the researcher?s theory? Explain your answer. HW 4 Score: 2. A food processing plant funnels its baked cookies into a sealing machine for packaging. In monitoring the process, the product manager assesses the quality of the seals by the proportion of defectives. The current ?sealer? has a defective rate of about 5% to 7%. The production manager thinks a higher temperature setting on the machine would improve the quality of the seals, so he designs an experiment to compare the two temperature settings (standard versus higher). From a day?s production run using the standard setting, 300 packages of cookies are randomly selected and assessed for sealing defects. Regretfully, such testing destroys the package (and the cookies). The following day, the sealing machine is set to the higher temperature and another sample of 300 packages is randomly chosen and tested. The number of defective seals is 20 for the standard temperature, 13 for the higher temperature. Let p1 = the proportion of defective seals for all cookies packaged at the standard temperature and p2 = the proportion of defective seals for all cookies packaged at the higher temperature. a. The production manager would like to test that the higher temperature does lead to an improved process (fewer defects) using a 10% level of significance. State the hypotheses to be tested. H0: __________________________________ Ha: __________________________________ b. If the null hypothesis is true, there is a common population proportion p. Give the estimate of the common population proportion of defects. c. Use the above estimate and determine the value of the test statistic and its symbol. Symbol Test Statistic = _____ = __________ d. The p-value is a probability computed assuming the null hypothesis is true. Probabilities can be interpreted as a long- term proportion. The p-value for this test is 0.108; interpret this p-value. If the experiment were repeated many times and ? e. What is the statistical decision? Circle one: Reject H0 Fail to Reject H0 Give the appropriate conclusion in the context of the problem. Kirsten Namesnik A study is designed to determine whether grades in a statistics course could be improved by offering special review material