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 5 for 95% confidence. The study was based on a random sample of 64 undergraduates.

1. (a) Give the 95% confidence interval.

2. (b) If you wanted 99% confidence for the same study, would your margin of error be greater than, equal to, or less than 5? Explain your answer.

Answer 1

= 78, E=5 c=95% n=64

a)

formula for confidence interval is

( - E ) < <  ( + E )

78 - 5   < < 78 + 5

73 < < 83

Confidence interval is = ( 73 , 83)

b)

greater than 5

A wider margin of eror is needed in order to be more confident that the interval include the true mean.

because,

for 95% confidence level the critical value is only 1.96

for 99% confidence level the critical value is increases to 2.58

due to this increase in critical value the margin of error for the 99% confidence level increases.