Question

Assume that a sample is used to estimate a population mean μμ. Find the 99.9% confidence interval for a sample of size 62 with a mean of 19.4 and a standard deviation of 12.3. Enter your answer as an open-interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

99.9% 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 = 3.457

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

= 3.457 * (12.3 / 62)

Margin of error = E = 5.4

The 99.9% confidence interval estimate of the population mean is,

- E < < + E

19.4 - 5.4 < < 19.4 + 5.4

14 < < 24.8

99.9% C.I. = (14 , 24.8)