A random sample of 80 companies who announced corrections to their balance sheets took a mean time of 8.1 days for the time between balance sheet construction and the complete audit.The standard deviation of these times was 1.3 days.What is the critical value for $\alpha$ = .001 to test the claim that $\mu$ is greater than 7.5 days.
A)2.575
B)3.09
C)-1.96
D)-2.575
E)-3.09

Question

Quizplus · Accepted Answer

First, we need to calculate the F-statistic:

$F=\frac{S_S^2}{S_E^2}=\frac{(n-1)S^2}{S_E^2}=\frac{(80-1)(1.3)^2}{(8.1-7.5)^2}=12.69$

Next, we need to find the critical value from the F-distribution with degrees of freedom (1,79) and alpha level .001:

$F_{critical}=F_{(1,79,.001)}=3.09$

Since our calculated F-statistic (12.69) is greater than the critical value (3.09), we reject the null hypothesis and conclude that there is evidence to support the claim that the mean time between balance sheet construction and complete audit is greater than 7.5 days.

A Random Sample of 80 Companies Who Announced Corrections to Their