In: Statistics and Probability
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.)
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)