## Construct the confidence interval for the population mean

Construct the confidence interval for the population mean .

c = 0.90, s = 17.8, s = 12.0, and n = 110

Solution

Use the Formula E =

to find the margin of error, where is the z-score corresponding to an area of c,

is the population standard deviation and

n is the sample size.

When n 30 you can use s in place of , where s is the sample standard deviation.

.

Substitute the value of c and evaluate to find the area in each tail.

= = 0.05

Use a standard normal table to find the positive critical value the corresponds to a tail area of 0.05

= 1.645

The population standard deviation is unknown but because n30, use s in place of .

Substitute the value 12.0, and n = 110 to find E.

E =

1.9

Use the margin of error to find the left endpoint.

Left endpoint = – E

= 17.8 – 1.9 = 15.9

Now find the right endpoint

Right endpoint = + E

= 17.8 + 1.9 = 19.7

Therefore,  a  90% confidence interval for is (15.9, 19.7).