Assume that a sample is used to estimate a population mean μ.
Find the 90% confidence interval for a sample of size 35 with a
mean of 55.8 and a standard deviation of 5.7.
Enter your answer as an open-interval
(i.e., parentheses) accurate to one decimal place.
An example of such an answer is "(66.9,82.4)".
90% C.I. =
Answer should be obtained without any preliminary rounding.
However, the critical value may be rounded to 3 decimal places.
Solution :
Given that,
t /2,df = 1.691
Margin of error = E = t/2,df * (s /n)
= 1.691 * (5.7 / 35)
Margin of error = E = 1.6
The 90% confidence interval estimate of the population mean is,
- E < < + E
55.8 - 1.6 < < 55.8 + 1.6
54.2 < < 57.4
90% C.I. (54.2 , 57.4)
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