You have constructed a 95% confidence interval to estimate the mean number of people downloading music files from the internet using a sample of 150 people.Which of the following statements is/are true?
I.A 95% Confidence interval will be wider than a 99% confidence interval.
II.Sampling a smaller number of people will increase the margin of error.
III.Changing the sample size will change the value of t*.

Question

You have constructed a 95% confidence interval to estimate the mean number of people downloading music files from the internet using a sample of 150 people.Which of the following statements is/are true? 
I.A 95% Confidence interval will be wider than a 99% confidence interval.
II.Sampling a smaller number of people will increase the margin of error.
III.Changing the sample size will change the value of t*.

Quizplus · Accepted Answer

I. A 95% confidence interval will be narrower than a 99% confidence interval because a higher confidence level requires a wider interval.
II. Sampling a smaller number of people will typically increase the margin of error because a smaller sample size reduces the precision of the estimate.
III. Changing the sample size will change the value of t* because it affects the degrees of freedom used to calculate the t-value used in the interval estimation formula. As the sample size increases, the degrees of freedom increase and t* decreases.

You Have Constructed a 95% Confidence Interval to Estimate the Mean