A vaccine to prevent a severe virus was given to children within the first year of life as part of a drug study. The study reported that of the 3323 children randomly assigned the vaccine, 54 got the virus. Of the 1659 children randomly assigned the placebo, 46 got the virus. a. Find the sample percentage of children who caught the virus in each group. Is the sample percentage lower for the vaccine group, as investigators hoped? b. Determine whether the vaccine is effective in reducing the chance of catching the virus, using a significance level of 0.01. The first few steps of the hypothesis-testing procedure are given. Complete the procedure. a Click the icon view the first few steps of the hypothesis-testing procedure. a. Find the sample percentage of children who caught the virus in the vaccine group. % (Round to two decimal places as needed.) O First Steps of Hypothesis-Testing Procedure Find the sample percentage of children who caught the virus in the placebo group. % (Round to two decimal places as needed.) The hypotheses are shown below, where p, is the proportion that gets the virus among those who take the vaccine, and p. is the proportion that get the virus among those who take a placebo. Is the sample percentage lower for the vaccine group, as investigators hoped? O Yes Hg: P = Pp H P,

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Chapter11: Data Analysis And Probability
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A vaccine to prevent a severe virus was given to children within the first year of life as part of a drug study. The study reported that of the 3323 children randomly assigned the vaccine, 54 got the virus. Of the 1659 children randomly assigned the placebo, 46 got the virus.
a. Find the sample percentage of children who caught the virus in each group. Is the sample percentage lower for the vaccine group, as investigators hoped?
b. Determine whether the vaccine is effective in reducing the chance of catching the virus, using a significance level of 0.01. The first few steps of the hypothesis-testing procedure are given. Complete the procedure.
1 Click the icon to view the first few steps of the hypothesis-testing procedure.
a. Find the sample percentage of children who caught the virus in the vaccine group.
% (Round to two decimal places as needed.)
First Steps of Hypothesis-Testing Procedure
Find the sample percentage of children who caught the virus in the placebo group.
% (Round to two decimal places as needed.)
The hypotheses are shown below, where p, is the proportion that gets the virus
among those who take the vaccine, and p, is the proportion that get the virus
Is the sample percentage lower for the vaccine group, as investigators hoped?
among those who take a placebo.
Ho: Pv = Pp
Ha: Pv <Pp
Yes
O No
Although we don't have a random sample, we do have random assignment to
b. Find the test statistic for this test.
groups.
(Round to two decimal places as needed.)
54 +46
100
2 0.020072
3323 + 1659
4982
Find the p-value for this test.
nyp = 3323(0.020072) 66.70, which is more than 10
%3D
n,p = 1659(0.020072) 33.30, which is more than 10 (and the other two
products are larger)
p-value =
(Round to three decimal places as needed.)
What is the conclusion for this test?
O A. Do not reject Ho. There is not sufficient evidence to conclude that the vaccine is effective in reducing the chance of catching the virus at the significance level of 0.01.
Print
Done
O B. Reject Ho. There is sufficient evidence to conclude that the vaccine is effective in reducing the chance of catching the virus at the significance level of 0.01.
O C. Do not reject Ho. There is sufficient evidence to conclude that the vaccine is effective in reducing the chance of catching the virus at the significance level of 0.01.
O D. Reject Ho. There is not sufficient evidence to conclude that the vaccine is effective in reducing the chance of catching the virus at the significance level of 0.01.
Transcribed Image Text:A vaccine to prevent a severe virus was given to children within the first year of life as part of a drug study. The study reported that of the 3323 children randomly assigned the vaccine, 54 got the virus. Of the 1659 children randomly assigned the placebo, 46 got the virus. a. Find the sample percentage of children who caught the virus in each group. Is the sample percentage lower for the vaccine group, as investigators hoped? b. Determine whether the vaccine is effective in reducing the chance of catching the virus, using a significance level of 0.01. The first few steps of the hypothesis-testing procedure are given. Complete the procedure. 1 Click the icon to view the first few steps of the hypothesis-testing procedure. a. Find the sample percentage of children who caught the virus in the vaccine group. % (Round to two decimal places as needed.) First Steps of Hypothesis-Testing Procedure Find the sample percentage of children who caught the virus in the placebo group. % (Round to two decimal places as needed.) The hypotheses are shown below, where p, is the proportion that gets the virus among those who take the vaccine, and p, is the proportion that get the virus Is the sample percentage lower for the vaccine group, as investigators hoped? among those who take a placebo. Ho: Pv = Pp Ha: Pv <Pp Yes O No Although we don't have a random sample, we do have random assignment to b. Find the test statistic for this test. groups. (Round to two decimal places as needed.) 54 +46 100 2 0.020072 3323 + 1659 4982 Find the p-value for this test. nyp = 3323(0.020072) 66.70, which is more than 10 %3D n,p = 1659(0.020072) 33.30, which is more than 10 (and the other two products are larger) p-value = (Round to three decimal places as needed.) What is the conclusion for this test? O A. Do not reject Ho. There is not sufficient evidence to conclude that the vaccine is effective in reducing the chance of catching the virus at the significance level of 0.01. Print Done O B. Reject Ho. There is sufficient evidence to conclude that the vaccine is effective in reducing the chance of catching the virus at the significance level of 0.01. O C. Do not reject Ho. There is sufficient evidence to conclude that the vaccine is effective in reducing the chance of catching the virus at the significance level of 0.01. O D. Reject Ho. There is not sufficient evidence to conclude that the vaccine is effective in reducing the chance of catching the virus at the significance level of 0.01.
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