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 thestatistics 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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