Question

A consumer advocate agency wants to find the mean repair cost of a washing machine. As part of the study 40 repair costs were selected and the mean repair cost was determined to be $150.00. From past studies the agency assumes that σ = $21. Construct a 90% confidence interval for the population mean. (Round confidence interval values to two decimal places.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = =$150.00

Population standard deviation =    = $21
Sample size = n =40

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2    * ( /n)

= 1.645* ( 21/   40)

= 5.46
At 90% confidence interval estimate of the population mean
is,

- E < < + E

150.00 - 5.46 <   <150.00 +5.46

144.54<   < 155.46

(  144.54,155.46)