Problem
The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 2.4 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.025 . Assume that the sample is a simple random sample selected from a normally distributed population. Complete parts (a) through (d) below. Click on the icon to view the data. a. Identify the null and alternative hypotheses. Choose the correct answer below. A. \[ \begin{array}{l} H_{0}: \sigma \geq 2.4 \text { minutes } \\ H_{A}: \sigma<2.4 \text { minutes } \end{array} \] c. \[ \begin{array}{l} H_{0}: \sigma=2.4 \text { minutes } \\ H_{A}: \sigma<2.4 \text { minutes } \end{array} \] \[ H_{A}: \sigma<2.4 \text { minutes } \] b. Compute the test statistic. \[ x^{2}=\square \] (Round to two decimal places as needed.) B. \[ \begin{array}{l} H_{0}: \sigma<2.4 \text { minutes } \\ H_{A}: \sigma=2.4 \text { minutes } \end{array} \] D. \[ \begin{array}{l} H_{0}: \sigma=2.4 \text { minutes } \\ H_{A}: \sigma \neq 2.4 \text { minutes } \end{array} \]
Solution
Step 1 ：The null hypothesis (H0) is a statement of no effect or no difference. The alternative hypothesis (HA) is what you might believe to be true or hope to prove true. In this case, we are testing the claim that the standard deviation of waiting times is less than 2.4 minutes. Therefore, the null hypothesis should be that the standard deviation is equal to or greater than 2.4 minutes, and the alternative hypothesis should be that the standard deviation is less than 2.4 minutes.
Step 2 ：The correct answer is \(H_{0}: \sigma \geq 2.4 \text { minutes }\) and \(H_{A}: \sigma<2.4 \text { minutes }\)
