Question

A study of stress on the campus of your university reported a mean stress level of 75 (on a 0 to 100 scale with a higher score indicating more stress) with a margin of error of 6 for 95% confidence. The study was based on a random sample of 64 undergraduates.

(a) Give the 95% confidence interval.

(______, ______)

(b) If you wanted 99% confidence for the same study, would your margin of error be greater than, equal to, or less than 6? Explain your answer.

It is impossible to determine if the margin of error will change using the information given.

The new margin of error would be greater than 6. A larger margin of error is needed to be more confident that the interval includes the true mean.

The new margin of error would be less than 6. A smaller margin of error is needed to be more confident that the interval includes the true mean.

The confidence level should never be changed for he same study.

The new margin of error would be equal to 6. The margin of error will not change when the confidence level is increased.

Answer 1

a) Since the margin of error is given as 6 and mean stress level as 75 then as we know that confidence interval is calculated as

Mean+-Error

=75+-6

={69, 81}

b) If we change the confidence level from 95 % to 99 % the margin of error increases because the Z score at 99 % confidence level is higher than at 95%. So,

The new margin of error would be greater than 6. A larger margin of error is needed to be more confident that the interval includes the true mean.