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.
(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 5? Explain your answer.
= 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.
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