A study of stress on the campus of your university reported a mean stress level
ID: 3061954 • Letter: A
Question
A study of stress on the campus of your university reported a mean stress level of 78 (on a 0 to 100 scale with a higher score indicating more stress) with a margin of error of 7 for 95% confidence. The study was based on a random sample of 49 undergraduates.
(a)
Give the 95% confidence interval.
If you wanted 99% confidence for the same study, would your margin of error be greater than, equal to, or less than 7? Explain your answer.
The new margin of error would be greater than 7. 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 equal to 7. The margin of error will not change when the confidence level is increased.
The new margin of error would be less than 7. A smaller margin of error is needed to be more confident that the interval includes the true mean.
It is impossible to determine if the margin of error will change using the information given.
The confidence level should never be changed for the same study.
Explanation / Answer
mean = 78 , ME = 7 , n = 49
a)
z value at 95%CI = 1.96
CI = mean +/- ME
= 78 + /- 7
= (71 , 85)
z value at 99% = 2.58
ME = 7
ME = z * ( s/sqrt(n))
7 = 2.58 * ( s/sqrt(49)
s = 18.99
CI = mean +/- z * ( s/sqrt(n))
= 78 +/- 2.58 * ( 18.99/sqrt(49))
= ( 71 , 85)
The new margin of error would be equal to 7. The margin of error will not change when the confidence level is increased.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.