Question

Suppose the random sample of waiting times at a bank listed below (minutes).

6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7
Use a 0.05 significance level to test the claim that these waiting times have a standard deviation less than 1.8 minutes. Draw a diagram illustrating your solution and show all work:

Answer 1

To test the claim that the waiting times have a standard deviation less than 1.8 minutes, a hypothesis test can be used. The null hypothesis is that the standard deviation is greater than or equal to 1.8 minutes, and the alternative hypothesis is that the standard deviation is less than 1.8 minutes. By calculating the sample standard deviation, test statistic, and critical value, a decision can be made.

Step-by-step explanation:

To test the claim that the waiting times have a standard deviation less than 1.8 minutes, we can use a hypothesis test. The null hypothesis (H0) is that the standard deviation is greater than or equal to 1.8 minutes, and the alternative hypothesis (Ha) is that the standard deviation is less than 1.8 minutes.

1. Calculate the sample standard deviation (s) of the waiting times.
2. Calculate the test statistic, which follows a chi-square distribution with (n-1) degrees of freedom, where n is the sample size.
3. Determine the critical value from the chi-square distribution table for the given significance level (0.05) and degrees of freedom.
4. Compare the test statistic with the critical value to make a decision.

In this case, we have a sample of 10 waiting times, so the degrees of freedom is (10-1) = 9. From the calculation, the test statistic is less than the critical value, which means we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the waiting times have a standard deviation less than 1.8 minutes.