Question

From public records, individuals were identified as having been charged with drunken driving not less than 6 months or more than 12 months from the starting date of the study. Two random samples from this group were studied. In the first sample of 30 individuals, the respondents were asked in a face-to-face interview if they had been charged with drunken driving in the last 12 months. Of these 30 people interviewed face to face, 16 answered the question accurately. The second random sample consisted of 44 people who had been charged with drunken driving. During a telephone interview, 27 of these responded accurately to the question asking if they had been charged with drunken driving during the past 12 months. Assume the samples are representative of all people recently charged with drunken driving. (a) Let p1 represent the population proportion of all people with recent charges of drunken driving who respond accurately to a face-to-face interview asking if they have been charged with drunken driving during the past 12 months. Let p2 represent the population proportion of all people who respond accurately to the question when it is asked in a telephone interview. Find a 90% confidence interval for p1 – p2. (Round your answers to three decimal places.) lower limit upper limit (b) Does the interval found in part (a) contain numbers that are all positive? all negative? mixed? Comment on the meaning of the confidence interval in the context of this problem. At the 90% level, do you detect any differences in the proportion of accurate responses to the question from face-to-face interviews as compared with the proportion of accurate responses from telephone interviews? Because the interval contains only positive numbers, we can say that there is a higher proportion of accurate responses in face-to-face interviews. Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of accurate responses in face-to-face interviews. We can not make any conclusions using this confidence interval. Because the interval contains only negative numbers, we can say that there is a higher proportion of accurate responses in telephone interviews. (c) Test the claim that there is a difference in the proportion of accurate responses from face-to-face interviews compared with the proportion of accurate responses from telephone interviews. Use ? = 0.05. (i) What is the level of significance? State the null and alternate hypotheses. H0: p1 = p2; H1: p1 ? p2 H0: p1 > p2; H1: p1 = p2 H0: p1 = p2; H1: p1 > p2 H0: p1 = p2; H1: p1 < p2 (ii) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference p1 ? p2. Round your answer to two decimal places.) (iii) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. (iv) Based on your answers to parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (v) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence to suggest that there is a difference in the proportion of accurate responses from face-to-face interviews compared with telephone interviews. Reject the null hypothesis, there is insufficient evidence to suggest that there is a difference in the proportion of accurate responses from face-to-face interviews compared with telephone interviews. Reject the null hypothesis, there is sufficient evidence to suggest that there is a difference in the proportion of accurate responses from face-to-face interviews compared with telephone interviews. Fail to reject the null hypothesis, there is insufficient evidence to suggest that there is a difference in the proportion of accurate responses from face-to-face interviews compared with telephone interviews.

Answer 1