# Thread: Testing of population varience

1. ## Testing of population varience

with an individual lines at its various windows , a post office finds that the standard deviation for normally distributed waiting times for customers on Friday afternoon is 7.2 minutes . The post office expreiemets with a single, main waiting line and finds that for a random sample of 25 customers, the waiting times for customers have a standard deviation of 3.5 minutes.

my chi square test value = 5.67 , but teh chi sqaure critical at α = 0.05 and v = 24 is 36.415 , i do n't have enough evidenvce to reject H0 ,
H0 = 7.2
H1= <7.2 ,

But the ans provided is REJECT H0 , why ?

I think the ans provided is incorrect , correct me if i am wrong .

2. ## Re: Testing of population varience

When writing out your hypotheses, please attend to precision and write them out correctly; $H_0 = c$ is not a proper hypothesis.

I believe you meant to state the following hypotheses:
$H_0: \sigma=7.2$, and
$H_1: \sigma < 7.2$.

This hypothesis test is a lower one-tailed test, which we observe from the alternative hypothesis.

The critical region for a lower one-tailed alternative is given by $T<\chi^2_{\alpha, N-1}$.

Your calculations appear to be correct, but you have confused the critical region with its complement (the acceptance region).

The book is right, but you were on the right path. Please attend to precision when doing mathematics, and you will likely avoid such careless errors in the future.

Good luck!
-Andy