Question

6.27  Average hours per week listening to the radio. The Student Monitor surveys 1200 undergraduates from four-year colleges and universities throughout the United States semiannually to understand trends among college students.¹¹ Recently, the Student Monitor reported that the average amount of time listening to the radio per week was 11.5 hours. Of the 1200 students surveyed, 83% said that they listened to the radio, so this collection of listening times has around 204 (17% × 1200) zeros. Assume that the standard deviation is 8.3 hours.

1. (a) Give a 95% confidence interval for the mean time spent per week listening to the radio.

2. (b) Is it true that 95% of the 1200 students reported weekly times that lie in the interval you found in part (a)? Explain your answer.

3. (c) It appears that the population distribution has many zeros and is skewed to the right. Explain why the confidence interval based on the Normal distribution should nevertheless be a good approximation.

Answer 1

Answer:

Given that:

The Student Monitor surveys 1200 undergraduates from four-year colleges and universities throughout the United States semiannually to understand trends among college students.¹¹ Recently, the Student Monitor reported that the average amount of time listening to the radio per week was 11.5 hours. Of the 1200 students surveyed, 83% said that they listened to the radio, so this collection of listening times has around 204 (17% × 1200) zeros. Assume that the standard deviation is 8.3 hours

a) Give a 95% confidence interval for the mean time spent per week listening to the radio.

95% confidence interval for the mean is C.I = ( 11.03, 11.97).

Standard error =

Standard error =

Standard error =

Consider 95% confidence interval Z=1.96

b) Is it true that 95% of the 1200 students reported weekly times that lie in the interval you found in part (a)? Explain your answer.

No, it is not true that 95% of the 1200 students reported weekly times lie in the interval we found in part (a).

Because If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean.

c) It appears that the population distribution has many zeros and is skewed to the right. Explain why the confidence interval based on the Normal distribution should nevertheless be a good approximation.

The confidence interval based on the normal distribution would not be a good estimation, because we have used z-critical value in the estimation of confidence interval which would not be appropriate.