Problem
A company claims that the mean monthly residential electricity consumption in a certain region is more than 880 kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 69 residential customers has a mean monthly consumption of $910 \mathrm{kWh}$. Assume the population standard deviation is $120 \mathrm{kWh}$. At $\alpha=0.05$, can you support the claim? Complete parts (a) through (e). A. \[ \begin{array}{l} H_{0}: \mu=910 \\ H_{a}: \mu \neq 910 \text { (claim) } \end{array} \] C. \[ \begin{array}{l} H_{0}: \mu>910 \text { (claim) } \\ H_{a}: \mu \leq 910 \end{array} \] E. \[ \begin{array}{l} H_{0}: \mu>880 \text { (claim) } \\ H_{a}: \mu \leq 880 \end{array} \] B. \[ \begin{array}{l} H_{0}: \mu \leq 910 \\ H_{a}: \mu>910 \text { (claim) } \end{array} \] D. \[ \begin{array}{l} H_{0}: \mu \leq 880 \\ H_{a}: \mu>880 \text { (claim) } \end{array} \] F. \[ \begin{array}{l} H_{0}: \mu=880 \text { (claim) } \\ H_{a}: \mu \neq 880 \end{array} \] (b) Find the critical value(s) and identify the rejection region(s). Select the correct choice below and fill in the answer box within your choice. Use technology. (Round to two decimal places as needed.) A. The critical value is B. The critical values are \pm
Solution
Step 1 ：The company claims that the mean monthly residential electricity consumption is more than 880 kWh. Therefore, the null hypothesis should be the opposite of the claim, i.e., the mean monthly residential electricity consumption is less than or equal to 880 kWh. The alternative hypothesis should be the claim itself, i.e., the mean monthly residential electricity consumption is more than 880 kWh.
Step 2 ：The correct null and alternative hypotheses are: \[H_{0}: \mu \leq 880\] \[H_{a}: \mu>880 \text { (claim) }\]
Step 3 ：Final Answer: \[\boxed{H_{0}: \mu \leq 880, H_{a}: \mu>880 \text { (claim) }}\]
