Calculate Some Confidence Intervals This Active Learning section provides some p

Question

Calculate Some Confidence Intervals This Active Learning section provides some practice in calculating confidence intervals. For this set of exercises, you are working with a survey of 1,000 people who responded to questions about satellite radio. The questions, sample statistics, and other pertinent information are listed below. Compute the 95% confidence interval for the population parameter in each case. Be certain to follow logic of the questions as it has implications for the sample size pertaining to each question.

Explanation / Answer

for 95% confidence interval ; z=1.96

1) for have you heard satellite radio:

p=0.5 ; n=1000

hence std error =(p*(1-p)/n)1/2 =0.0158

hence 95% confidence interval =p -/+ z*std error =0.4690 ; 0.5310

2) for owning of satellite radio ; p=0.3 ; n=500

std error =(p*(1-p)/n)1/2 =0.0205

hence 95% confidence interval =p -/+ z*std error =0.2598 ; 0.3402

3)

for number of minutes of listening of satellite radio

std error=std deviation/(n)1/2 =25/(150)1/2 =2.0412

therefore 95% confidence interval =sample mean -/+ z*std error =96.6992 ; 104.7008

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