Question

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% confidence interval for the population mean.

A random sample of 60 home theater systems has a mean price of ​$110.00. Assume the population standard deviation is ​$16.90.

The​ 90% confidence interval is what?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 110

Population standard deviation =    = 16.90
Sample size = n =60

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2    * ( /n)

= 1.645* (16.90 /  60 )

= 3.59
At 90% confidence interval
is,

- E < < + E

110 - 3.59 <   < 110+ 3.59

106.41 <   < 113.59