5 Suppose a bond proposal for school construction will be submitted to voters at the next municipal election. A major portion of the money will be used to build schools in a rapidly \"developing\" section of the city whereas the remaining money will be used to update current school buildings. To assess the viability of the proposal, a random sample of 50 residents who live in the developing section of the city was selected and an independent random sample of 100 residents who do not live in the developing section of the city was selected. All 150 residents were asked how they plan to vote for the proposal. The results are summarized below. Let p1 represent the population proportion of all residents of the developing section that are in favor of the proposal, and p2 represent the population proportion of all residents from outside the developing section that are in favor of the proposal. 5.a Estimate the difference in the two population proportions p1 - p2. 5.b Provide the 99% confidence interval estimate for the difference in the population rate of favoring the proposal for all residents of the developing section as compared to all residents from outside the developing section. 5.c A 90% confidence interval based on the same data would result in an interval that is ___________ the 99% confidence interval. wider than narrower than the same width as 5.d The computation of the 99% confidence interval, which involved using a z* multiplier, requires a check that the sample sizes are large enough. Which of the following is the correct check at that condition? The sample sizes of 50 and 100 are both at least 10. The sample sizes of 50 and 100 are both at least 30. The values of 50, 100, 38, and 65 are all at least 10. The values of 38, 12, 65, and 35 are all at least 10. ------------------------------------------------------------------------------------------------------------------------------------------ Question 6 \"Have you ever refused a job, promotion, or transfer because it would lead to spending less time with your family?\" This question was asked in a survey of two independent random samples representing two populations: Population 1: all working adults living in the East with a family of at least two children Population 2: all working adults living in the Midwest with a family of at least two children The researcher would like to assess if the proportion of all such working adults living in the East who have refused a job for this reason would exceed the same proportion for all such working adults living in the Midwest. The significance level is set to 5%. The results of the study are summarized below. 6.a The researcher sets up the null hypothesis as H0: p1 = p2. Select the appropriate alternative hypothesis. Ha: p1 not equal to p2 Ha: p1 > p2 Ha: p1 < p2 6.b It is important to understand what the various parameters in the hypotheses represent. Consider the following incorrect definition for the parameter p1. \"p1 is the sample proportion of working adults from the East who have refused a job for this reason.\" Provide the two words to complete this statement: This definition would be correct if you replace the word _____________ with the word _______________. 6.c The test statistic is computed assuming the null hypothesis is true, that is, p1 = p2 = p. Which of the following is the best estimate of that common proportion p? 0.1085 0.23605 0.2376 0.4721 6.d It seems that the sample sizes of 93 and 88 should be sufficiently large enough to use a normal approximation to compute the p-value. Provide verification that the sample sizes are large enough. Student answer No answer entered. 6.e The z test statistic value is 1.71. Find the corresponding p-value. Include a complete sketch to show the p-value. (You may make your own complete sketch by hand and upload image as a .jpg or use either the prob() script or even better pval() script in R to create the picture for you.) Then below the (inserted image) sketch provide the actual value by writing "p-value = _________." 6.f At a 5% significance level, the decision is to reject the null hypothesis. Which of the following word(s) should be used to complete the appropriate one sentence conclusion in the context of the problem? For the populations represented by our samples, there ___________ sufficient evidence to support that the population proportion of all working adults living in the East (with at least two children) who have refused a job for this reason exceeds that for all working adults living in the Midwest (with at least two children). IS IS NOT