Problem
01 $=2$ 3 4 5 6 7 8 10 A somewhat outdated study indicates that the mean number of hours worked per week by software developers is 44 . We have good reason to suspect that the mean number of hours worked per week by software developers, $\mu$, is now different from 44 and wish to do a statistical test. We select a random sample of soltware developers and find that the mean of the sample is 40 hours and that the standard deviation is 6 hours. Based on this information, complete the parts below. (a) What are the null hypothesis $H_{0}$ and the alternative hypothesis $H_{1}$ that should be used for the test? \[ \begin{array}{l} H_{0}: \mu=44 \\ H_{1}: \mu<44 \end{array} \] (b) Suppose that we deode to reject the null hypothesis. What sort of error might we be making? Trpe 1 (c) Suppose the true mean number of hours worked by soltware engineers is 44 hours. Fill in the blanks to describe a Type 1 error. A Tvpe 1 irror vould be rejecting the hypothesis that $\mu$ is equal to 44 when, in fact, $\mu$ is (Choose one) Submit Assignn Conthue
Solution
Step 1 ：(a) The null hypothesis $H_{0}$ is that the mean number of hours worked per week by software developers, $\mu$, is 44. The alternative hypothesis $H_{1}$ is that the mean number of hours worked per week by software developers, $\mu$, is not 44.
Step 2 ：(b) If we decide to reject the null hypothesis, we might be making a Type I error.
Step 3 ：(c) If the true mean number of hours worked by software developers is 44 hours, a Type I error would be rejecting the hypothesis that $\mu$ is equal to 44 when, in fact, $\mu$ is 44.
