A survey of Internet users reported that 22% downloaded music onto their compute
ID: 3131336 • Letter: A
Question
A survey of Internet users reported that 22% 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 30% 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.)
Also report a 95% confidence interval for the difference in proportions. (Round your answers to four decimal places.)
Explanation / Answer
Formulating the hypotheses
Ho: p1 - p2 >= 0
Ha: p1 - p2 < 0
Here, we see that pdo = 0 , the hypothesized population proportion difference.
Getting p1^ and p2^,
p1^ = x1/n1 = 0.22
p2 = x2/n2 = 0.3
Also, the standard error of the difference is
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.016445257
Thus,
z = [p1 - p2 - pdo]/sd = -4.864624367 [ANSWER, Z]
Also, the p value is
P = 5.73372E-07 [ANSWER, P VALUE]
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For the 95% confidence level, then
alpha/2 = (1 - confidence level)/2 = 0.025
z(alpha/2) = 1.959963985
Margin of error = z(alpha/2)*sd = 0.032232112
lower bound = p1^ - p2^ - z(alpha/2) * sd = -0.112232112
upper bound = p1^ - p2^ + z(alpha/2) * sd = -0.047767888
Thus, the confidence interval is
( -0.112232112 , -0.047767888 ) [ANSWER, CONFIDENCE INTERVAL]
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