Question

A simple random sample of size nequals 14 is drawn from a population that is normally distributed. The sample mean is found to be x overbar equals 65 and the sample standard deviation is found to be sequals 16. Construct a 90 ​% confidence interval about the population mean.

The lower bound is

The upper bound is

​(Round to two decimal places as​ needed.)

Answer 1

Solution :

Given that,

t /2,df = 1.771

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

= 1.771 * (16 / 14)

Margin of error = E = 7.57

The 90% confidence interval estimate of the population mean is,

- E < < + E

65 - 7.57 < < 65 + 7.57

57.43 < < 72.57

The lower bound is 57.43

The upper bound is 72.57