The Student Monitor surveys 1185 undergraduates from four-year colleges and univ

Question

The Student Monitor surveys 1185 undergraduates from four-year colleges and universities throughout the United States semiannually to understand trends among college students. Recently, the Student Monitor reported that the average amount of time listening to the radio per week was 11.3 hours. Of the 1185 students surveyed, 83% said that they listened to the radio, so this collection of listening times has around 201 (17%×1185) zeros. Assume that the standard deviation is 8.2 hours.

a) Give a 90% confidence interval (±0.01) for the mean time spent per week listening to the radio.

The 90% confidence interval is from____ to_____ hours.

b) Is it true that 90% of the 1185 students reported weekly times that lie in the interval you found in part (a)? Yes or No

Explanation / Answer

a) here mean =11.3

and std error of mean for 1185 students =std deviation/(n)1/2 =0.2382

for 90% CI, z=1.6449

hence confidence interval =point estimate -/+ z*Std error =10.9082 ; 11.6918

b) here p=0.83

and std error =(p(1-p)/n)1/2 =0.0109

confidence interval of proportion =point estimate -/+ z*Std error =0.8121 ; 0.8479

hence it does not contain 90% of the students

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