A survey of Internet users reported that 19% downloaded music onto their compute

Question

A survey of Internet users reported that 19% downloaded music onto their computers. The of lawsuits by the recording industry may be a reason why this percent has decreased from the estimate of 25% from a survey taken two years before. Suppose we are not exactly sure about the sizes of the samples. Perform the calculations for the tests and 95% confidence intervals under each of the following assumptions. (Use previous recent. Round your test statistics to two decimal places and your confidence Intervals to four decimal places.) Both sample sizes are 1000.

Explanation / Answer

(i) p1=0.25 ; n1=1000

p2=0.19 ; n2=1000

std error =(p1(1-p1)/n1+p2(1-p2)/n2))1/2 =0.0185

hence test stat z=(p1-p2)/std error =3.25

for 95% CI, z=1.96

hence confidence interval =mean +/- z*std error =0.0238 ; 0.0962

(ii)

p1=0.25 ; n1=1600

p2=0.19 ; n2=1600

std error =(p1(1-p1)/n1+p2(1-p2)/n2))1/2 =0.0146

hence test stat z=(p1-p2)/std error =4.11

for 95% CI, z=1.96

hence confidence interval =mean +/- z*std error =0.0314 ; 0.0886

c)

p1=0.25 ; n1=1000

p2=0.19 ; n2=1600

std error =(p1(1-p1)/n1+p2(1-p2)/n2))1/2 =0.0168

hence test stat z=(p1-p2)/std error =3.56

for 95% CI, z=1.96

hence confidence interval =mean +/- z*std error =0.0270 ; 0.0930

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