Question

Assume that a sample is used to estimate a population mean μμ. Find the 99.5% confidence interval for a sample of size 61 with a mean of 34.5 and a standard deviation of 7.4. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places.

99.5% C.I. = ?

The answer should be obtained without any preliminary rounding.

Answer 1

Solution :

Given that,

t /2,df = 2.915

Margin of error = E = t/2,df * (s /n)

= 2.915 * (7.4 / 61)

Margin of error = E = 2.762

The 99.5% confidence interval estimate of the population mean is,

- E < < + E

34.5 - 2.762 < < 34.5 + 2.762

31.738 < < 37.262

99.5% C.I. = (31.738 , 37.262)