Question

In a random sample of 36 CD players brought in for repair, the average repair cost was $80 and the standard deviation (S) of repair costs was $14. Use a significance level of 0.01 to test the claim that the average repair cost is less than $85.

Answer 1

Solution :-

Given :-

Mean ( u ) = 85

Sample mean ( ) = 80

Sample Std Deviation ( s ) = 14

Sample Size ( n ) = 36.

DF = n - 1 = 36 - 1 = 35

Significance level ( ) = 0.01

Hypothesis :-

Ho : u = 85

H1 : u < 85

SE = s / n

SE = 14   36

SE = 2.33

Test Statistic :

t = - u / SE

t = 80 - 85 / 2.33

t = - 2.143

By using P - Value Approach

P- Value at t = -2.143 and DF = 35

P- Value = 0.0196

Since, P - Value ( 0.0196 ) > ( 0.01 )

Decision : Fail to reject Ho

Conclusion :- Therefore, there is not enough evidence to claim that the population mean μ is less than 85, at the 0.01 significance level.