Question

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.

Answer 1

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)