4b) Conduct a test at the α=0.01 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p1>p2. The sample data are x1=117, n1=242, x2=131, and n2=312. (b) Determine the test statistic. z0= (Round to two decimal places as needed.)
5) Conduct the following test at the α=0.10 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume that the samples were obtained independently using simple random sampling. Test whether p1≠p2. Sample data are x1=28, n1=255, x2=38, and n2=302. (b) The test statistic z0 is (Round to two decimal places as needed.)
6) Construct a confidence interval for p1−p2 at the given level of confidence. x1=354, n1=516, x2=442, n2=566, 95% confidence. The researchers are % confident the difference between the two population proportions, p1−p2, is between and (Use ascending order. Type an integer or decimal rounded to three decimal places as needed.)
7) Construct a confidence interval for p1−p2 at the given level of confidence. x1=35, n1=237, x2=30, n2=277, 90% confidence. The researchers are % confident the difference between the two population proportions, p1−p2, is between and (Use ascending order. Type an integer or decimal rounded to three decimal places as needed.)
10) In 2003, an organization surveyed 1,510 adult Americans and asked about a certain war, "Do you believe the United States made the right or wrong decision to use military force?" Of the 1,510 adult Americans surveyed, 1,090 stated the United States made the right decision. In 2008, the organization asked the same question of 1,510 adult Americans and found that 575 believed the United States made the right decision. Construct and interpret a 90% confidence interval for the difference between the two population proportions, p2003−p2008. The lower bound of a 90% confidence interval is (Round to three decimal places as needed.)
11) In clinical trials of a medication, 2136 subjects were divided into two groups. The 1590 subjects in group 1 received the medication. The 546 in group 2 received a placebo. Of the 1590 subjects in group 1, 66 experienced dizziness as a side effect. In group 2, 20 experienced dizziness as a side effect. To test whether the proportion experiencing dizziness in group 1 is greater than that in group 2, the researchers entered the data into statistical software and obtained the following results. Test at α=0.05. Sample X N Sample p Estimate for p(1)−p(2): 0.004879 1 66 1590 0.041509 95% CI for p(1)−p(2): (−0.013679, 0.023437) 2 20 546 0.03663 Test for p(1)−p(2)=0 (vs>0): z=0.50 P-value=0.308 What conclusion can be drawn at the α=0.05 level of significance? A. Reject H0, there is enough evidence to conclude that the proportion experiencing dizziness in group 1 is greater than the proportion experiencing dizziness in group 2. B. Do not reject H0, there is not enough evidence to conclude that the proportion experiencing dizziness in group 1 is greater than the proportion experiencing dizziness in group 2. C. Do not reject H0, there is enough evidence to conclude that the proportion experiencing dizziness in group 1 is greater than the proportion experiencing dizziness in group 2. D. Reject H0, there is not enough evidence to conclude that the proportion experiencing dizziness in group 1 is greater than the proportion experiencing dizziness in group 2.
12) A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained if he wishes the estimate to be within three percentage points with 95% confidence, assuming that (a) he uses the estimates of 21.7% male and 18.1% female from a previous year? (b) he does not use any prior estimates? (a) n= (Round up to the nearest whole number.) b)