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Question 22 of 66\newlineThis question: 11 point(s) possible\newlineA company claims that the mean monthly residential electricity consumption in a certain region is more than 860kWh860 \, \text{kWh}. You want to test this claim. You find that a random sample of 6565 residential customers has a mean monthly consumption of 890kWh890\,\text{kWh}. Assume the population standard deviation is 128kWh128\,\text{kWh}. At α=0.01\alpha=0.01, can you support the claim? Complete parts (a) through ( 00 ).\newline(a) Identify H0H_{0} and HaH_{a}. Choose the correct answer below.\newlineA.\newline{H0:μ>860(claim) H2:μ860\begin{cases} H_{0}:\mu > 860 \, \text{(claim)} \ H_{2}:\mu \leq 860 \end{cases}\newlineB.\newline{H0:μ>890(claim) Ha:μ890\begin{cases} H_{0}:\mu > 890 \, \text{(claim)} \ H_{a}:\mu \leq 890 \end{cases}\newlineC.\newline{H0:μ890 Ha:μ>890(claim)\begin{cases} H_{0}:\mu \leq 890 \ H_{a}:\mu > 890 \, \text{(claim)} \end{cases}\newlineD.\newline656500\newlineE.\newline656511\newlineF.\newline656522

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Q. Question 22 of 66\newlineThis question: 11 point(s) possible\newlineA company claims that the mean monthly residential electricity consumption in a certain region is more than 860kWh860 \, \text{kWh}. You want to test this claim. You find that a random sample of 6565 residential customers has a mean monthly consumption of 890kWh890\,\text{kWh}. Assume the population standard deviation is 128kWh128\,\text{kWh}. At α=0.01\alpha=0.01, can you support the claim? Complete parts (a) through ( 00 ).\newline(a) Identify H0H_{0} and HaH_{a}. Choose the correct answer below.\newlineA.\newline{H0:μ>860(claim) H2:μ860\begin{cases} H_{0}:\mu > 860 \, \text{(claim)} \ H_{2}:\mu \leq 860 \end{cases}\newlineB.\newline{H0:μ>890(claim) Ha:μ890\begin{cases} H_{0}:\mu > 890 \, \text{(claim)} \ H_{a}:\mu \leq 890 \end{cases}\newlineC.\newline{H0:μ890 Ha:μ>890(claim)\begin{cases} H_{0}:\mu \leq 890 \ H_{a}:\mu > 890 \, \text{(claim)} \end{cases}\newlineD.\newline656500\newlineE.\newline656511\newlineF.\newline656522
  1. Define Hypotheses: When conducting a hypothesis test, the null hypothesis (H0H_0) is a statement of no effect or no difference, and it is what we assume to be true before collecting any data. The alternative hypothesis (HaH_a) is what we want to test for - it is the claim that there is an effect or a difference. In this case, the company claims that the mean monthly residential electricity consumption is more than 860860 kWh. Therefore, the null hypothesis should reflect the opposite of this claim, and the alternative hypothesis should reflect the claim itself.
  2. Formulate Hypotheses: The correct null and alternative hypotheses are as follows:\newlineH0:μ860H_0: \mu \leq 860 (The mean is less than or equal to 860860 kWh, which is the opposite of the claim.)\newlineHa:μ>860H_a: \mu > 860 (The mean is greater than 860860 kWh, which is the claim.)\newlineTherefore, the correct answer is the one that reflects these hypotheses.
  3. Check Options: Looking at the options provided, we can see that option F states:\newlineH0:μ860H_0: \mu \leq 860\newlineHa:μ>860H_a: \mu > 860 (claim)\newlineThis matches our correct formulation of the null and alternative hypotheses.

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