Question: The human resources department of a large investment bank announced that the number of people it…

The human resources department of a large investment bank announced that the number of people it interviews monthly has a mean of 115 with a standard deviation of 17. The management of the bank suspects that the standard deviation exceeds 17. Suppose that the management wants to take a small sample of months and carry out a hypothesis test to see if its suspicions have support. State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) that it would use for this test.

\[ H_0: \quad \]

\[ H_1: \quad \]

\[ \begin{array}{|c|c|c|} \hline \mu & \bar{x} & p \\ \hline \hat{p} & \sigma & s \\ \hline \end{array} \]

Solution

The problem asks for the formulation of the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) regarding the standard deviation of the number of people interviewed monthly. The null and alternative hypotheses are based on whether the standard deviation exceeds 17. For this test, the hypotheses would be: Null hypothesis (\( H_0 \)): \[ \sigma = 17 \] Alternative hypothesis (\( H_1 \)): \[ \sigma > 17 \] The bank suspects that the standard deviation exceeds 17, prompting the one-tailed test with these hypotheses.