A survey of Internet users reported that 22% downloaded music onto their compute

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 31% from a survey taken two years before. Assume that the sample sizes are both 1371. 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.)

Summarize your conclusion.

A. We conclude that the proportions are different.

B. We conclude that the means are not different.    

C. We conclude that the proportions are not different.

D. We conclude that the means are different.

E. 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.

A. The interval gives us an idea of how large the difference is between the first survey and the second survey.

B. The interval shows no significant change in music downloads.    

C. The significance test does not indicate the direction of change, but the interval shows that the music downloads decreased.

D. The interval tells us there was a significant change in music downloads, but the test statistic is inconclusive.

E. The interval does not provide any more information than the significance test would tell us.

z = P-value =

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 0

Hypothesis test results:

95% confidence interval results:

Hence,

z = -5.34

p = 0.0000

We conclude that the proportions are different. Option A is correct.

95% confidence interval: (-0.1229, -0.0571)

The significance test does not indicate the direction of change, but the interval shows that the music downloads decreased. Option C is correct.

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 301.62 1371 425.01 1371 -0.09 0.016856324 -5.3392423 <0.0001

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