(a) Let p 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 p: 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 p-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 i 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 x = 0.05. (1) What is the level of significance? State the null and alternate hypotheses. Ho: P = p; Hi: p₁ = p He: P = P H: P₁ > P₂ H: Pi>P; H: P = p He: P = Pz H: P₁ < P₂ (ii) What sampling distribution will you use? What assumptions are you making? 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 known standard deviations. The Student's t. 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 unknown standard deviations. What is the value of the sample test statistic? Compute the correspond (Test the difference p₁ - p. Round your answer to two decimal places.) (iii) Find (or estimate) the P-value. (Round your answer to four decimal places.) t value as appropriate.