Question

A survey of Internet users reported that 17% 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. Suppose we are not exactly sure about the sizes of the samples. Perform the calculations for the significance 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.)

(i) Both sample sizes are 1000.

Z=

95% Confidence Interval=

(ii) Both sample sizes are 1600.

Z=

95% Confidence Interval=

(iii) The sample size for the survey reporting 31% is 1000 and the sample size for the survey reporting 17% is 1600.

Z=

95% Confidence Interval=

Answer 1

Previous :

: Proportion of internet users downloaded music on to their computers = 31/100 = 0.31

Recent:

: Proportion of internet users downloaded music on to their computers = 17/100 = 0.17

(i) Both sample sizes are 1000 i.e n₁ = 1000; n₂ = 1000

Z= 7.4304

Formula for confidence interval for difference of two population proportions : p₁ -p₂

for 95% confidence level = (100-95)/100 = 0.05

/2 = 0.05/2 =0.025

Z_0.025 = 1.96

95% confidence interval:

95% Confidence Interval= (10.1031, 0.1769) or (10.31%, 17.69%)

(ii) Both sample sizes are 1600.

Z= 9.3988

95% Confidence Interval=

95% Confidence Interval= (0.1108 , 0.1692) =(11.08%, 16.92%)

(iii) The sample size for the survey reporting 31% is 1000 and the sample size for the survey reporting 17% is 1600.

z= 8.0549

95% Confidence Interval=

95% Confidence Interval= (0.1059,0.1741) or (10.59% , 17.41%)