# Free Solved Statistics Problems

With individual lines at the checkouts, a store manager finds that the standard deviation for the waiting times on Monday mornings is 5.2 minutes. After switching to a single waiting line, he finds that for a random sample of 29 customers, the waiting times have a standard deviation of 5.9 minutes. Use a 0.05 significance level to test the claim that with a single line, waiting times vary less than with individual lines.

**Solution: **We need to test

_{}

We use the Chi-Square statistics

_{}

The critical Chi-Square value for 28 degrees of freedom, and_{} is equal to 41.337. Since the_{}statistics is less than the critical value, we fail to reject the null hypothesis. In other words, there's not enough evidence to support the claim that with a single line, waiting times vary less than with individual lines

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