33\' +-0.69 points MintroStat98.?.512XP My Notes Ask Your Teacher A survey of In

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33' +-0.69 points MintroStat98.?.512XP My Notes Ask Your Teacher 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 1381. 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.) 2- P-value Summarize your conclusion. O We conclude that the means are not different. O We conclude that the proportions are different. O We conclude that the proportions are not different. O We cannot draw any conclusions using a significance test for this data. We conclude that the means are different. 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. O The interval gives us an idea of how large the difference is between the first survey and the second survey. O The interval shows no significant change in music downloads. O The significance test does not indicate the direction of change, but the interval shows that the music downloads decreased. O The interval tells us there was a significant change in music downloads, but the test statistic is inconclusive. O The interval does not provide any more information than the significance test would tell us.

Explanation / Answer

Old Population:

xo = 0.31

n1 = 1381

s1 = (0.31*(1-0.31)/1381)1/2 = 0.012

New Population:

xn = 0.22

n2 = 1381

s2 = (0.22*(1-0.22)/1381)1/2 = 0.011

Effective Std Deviation (sp) = ((n1-1)*s12 + (n2-1)*s22 )/(n1+n2-2) = 0.012

Null And Alternate Hypothesis

H0: µo - µn = 0

Ha: µo - µn < 0

Test Statistic

z = (xo - xn)/(sp2/n1 + sp2/n2)1/2 = 205.45

p-value = TDIST(205.45,1381+1381-2,1) < 0.05

Since, p-value < 0.05, we reject the null hypothesis ie New population proportion has decreased than its original value.

We conclude that the proportions are different.

CI: xo - xn +/- 1.96*(0.012/13811/2) = (0.089,0.091)

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