A researcher studied the accuracy of responses on questions involving sensitive material. 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 34 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 34 people interviewed face-to-face, 15 answered the question accurately. The second random sample consisted of 43 people who had been charged with drunken driving. During a telephone interview, 21 of these responded accurately to the question asking if they had been charged with drunken driving during the past 12 months. Assume that the samples are representative of all people recently charged with drunken driving. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some cases, this choice will increase the P-value by a small amount or increase the length of the confidence interval, thereby making the answer slightly more "conservative."(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 people who respond accurately to the same question when it is asked in a telephone interview. Find a 90% confidence interval for p1 − p2. (Round your answers to four 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?Since the interval contains both positive and negative values, we can conclude, at the 90% level, that there is no significant difference between the proportion of accurate responses in face-to-face interviews and the proportion in telephone interviews.Since the interval contains only positive values, we can conclude, at the 90% level, that the proportion of accurate responses for face-to-face interviews is greater than that for telephone interviews. Since the interval contains only negative values, we can conclude, at the 90% level, that the proportion of accurate responses for face-to-face interviews is less than that for 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 α = 0.05.(i) What is the level of significance? State the null and alternate hypotheses.H0: μ1 ≠ μ2; H1: μ1 = μ2H0: μ1 > μ2; H1: μ1 < μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2H0: μ1 < μ2; H1: μ1 > μ2H0: μ1 = μ2; H1: μ1 < μ2 (ii) What sampling distribution will you use? What assumptions are you making?We will use the standard normal distribution. We assume that d has a normal distribution and that σ1 and σ2 are known.We will use the standard normal distribution. We assume the number of trials must be sufficiently large. We will use the standard normal distribution. We assume that both population distributions are approximately normal and that σ1 and σ2 are known.We will use Student's t distribution. We assume that d has a normal distribution and that σ1 and σ2 are unknown.We will use Student's t distribution. We assume that both population distributions are approximately normal and that σ1 and σ2 are unknown. What is the value of the sample test statistic? (Round your answer to two decimal places.) (iii) Find the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.
A researcher studied the accuracy of responses on questions involving sensitive material. 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 34 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 34 people interviewed face-to-face, 15 answered the question accurately. The second random sample consisted of 43 people who had been charged with drunken driving. During a telephone interview, 21 of these responded accurately to the question asking if they had been charged with drunken driving during the past 12 months. Assume that the samples are representative of all people recently charged with drunken driving. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some cases, this choice will increase the P-value by a small amount or increase the length of the confidence interval, thereby making the answer slightly more "conservative."
(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 people who respond accurately to the same question when it is asked in a telephone interview. Find a 90% confidence interval for p1 − p2. (Round your answers to four 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?
Since the interval contains both positive and negative values, we can conclude, at the 90% level, that there is no significant difference between the proportion of accurate responses in face-to-face interviews and the proportion in telephone interviews.
Since the interval contains only positive values, we can conclude, at the 90% level, that the proportion of accurate responses for face-to-face interviews is greater than that for telephone interviews.
Since the interval contains only negative values, we can conclude, at the 90% level, that the proportion of accurate responses for face-to-face interviews is less than that for 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 α = 0.05.
(i) What is the level of significance?
State the null and alternate hypotheses.
H0: μ1 ≠ μ2; H1: μ1 = μ2
H0: μ1 > μ2; H1: μ1 < μ2
H0: μ1 = μ2; H1: μ1 ≠ μ2
H0: μ1 < μ2; H1: μ1 > μ2
H0: μ1 = μ2; H1: μ1 < μ2
(ii) What sampling distribution will you use? What assumptions are you making?
We will use the standard
We will use the standard normal distribution. We assume the number of trials must be sufficiently large.
We will use the standard normal distribution. We assume that both population distributions are approximately normal and that σ1 and σ2 are known.
We will use Student's t distribution. We assume that d has a normal distribution and that σ1 and σ2 are unknown.
We will use Student's t distribution. We assume that both population distributions are approximately normal and that σ1 and σ2 are unknown.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(iii) Find the P-value. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
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