A survey of Internet users reported that 18% downloaded music onto their compute
ID: 3060052 • Letter: A
Question
A survey of Internet users reported that 18% downloaded music onto their computers. The filing of lawsuits by the recording industry may be a reason why this percent has decreased from the estimate of 26% from a survey taken two years before. Assume that the sample sizes are both 1411. Using a significance test, evaluate whether or not there has been a change in the percent of Internet users who download music. Provide all details for the test. (Round your value for z to two decimal places. Round your P-value to four decimal places.) z = P-value = Summarize your conclusion. We conclude that the proportions are different. We conclude that the means are different. We conclude that the proportions are not different. We conclude that the means are not different. We cannot draw any conclusions using a significance test for this data. Also report a 95% confidence interval for the difference in proportions. (Round your answers to four decimal places.) , Explain what information is provided in the interval that is not in the significance test results. The interval gives us an idea of how large the difference is between the first survey and the second survey. The interval tells us there was a significant change in music downloads, but the test statistic is inconclusive. The interval shows no significant change in music downloads. The interval does not provide any more information than the significance test would tell us. The significance test does not indicate the direction of change, but the interval shows that the music downloads decreased.
Explanation / Answer
H0: p1 = p2
H0 : p1 > p2
Pooled sample proportion (P) = (p1 * n1 + p2 * n2)/(n1 + n2)
= (0.26 * 1411 + 0.18 * 1411)/(1411 + 1411)
= 0.22
SE = sqrt(P * (1 - P) * (1/n1 + 1/n2))
= sqrt(0.22 * (1 - 0.22) * (1/1141 + 1/1141))
= 0.017
The test statistic z = (p1 - p2)/SE
= (0.26 - 0.18)/0.017 = 4.71
P-value = P(Z > 4.17)
= 1 - P(Z < 4.17)
= 1 - 1 = 0
As the p-value is less than the significance level (0 < 0.05), so the null hypothesis is rejected.
So we can concluded that the proportions are different.
At 95% confidence interval the critical value is z0.025 = 1.96
The 95% confidence interval is
p1 - p 2 +/- z0.025 * SE
= (0.26 - 0.18) +/- 1.96 * 0.017
= 0.08 +/- 0.0333
= 0.0467, 0.1133
As the interval doesn't cointain the hypothised value 0, so the null hypothesis is rejected.
Option - A is correct.
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