A company claims that the mean monthly residential electricity consumption in a certain region is more than 860 kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 66 residential customers has a mean monthly consumption of 900 kWh. Assume the population standard deviation is 123 kWh. At a= 0.10, can you support the claim? Complete parts (a) through (e). O A. Ho u= 860 (claim) H u# 860 O B. Ho: u> 900 (claim) H us 900 O C. Ho: = 900 Ha u# 900 (claim) YD. Ho: us860 H3 p> 860 (claim) OE Ho us 900 H p> 900 (claim) OF. Ho H> 860 (claim) H us 860 (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.) O A. The critical values are + OB. The critical value is

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**Hypothesis Testing of Mean Monthly Residential Electricity Consumption**

A company claims that the mean monthly residential electricity consumption in a certain region is more than 860 kilowatt-hours (kWh). You want to test this claim. You find that a random sample of 66 residential customers has a mean monthly consumption of 900 kWh. Assume the population standard deviation is 123 kWh. At a significance level (\(\alpha\)) of 0.10, can you support the claim? Complete parts (a) through (e).

---

**Part (a):**
Define the null and alternative hypotheses:

- **Option A**:
  \[
  H_0: \mu \neq 860 \quad (\text{claim}) \\
  H_a: \mu \neq 860
  \]

- **Option B**:
  \[
  H_0: \mu \geq 900 \quad (\text{claim}) \\
  H_a: \mu < 900
  \]

- **Option C**:
  \[
  H_0: \mu \neq 900 \\
  H_a: \mu \neq 900 \quad (\text{claim})
  \]

- **Option D**:
  \[
  H_0: \mu \leq 860 \\
  H_a: \mu > 860 \quad (\text{claim}) \quad \text{(Selected)}
  \]

- **Option E**:
  \[
  H_0: \mu \geq 860 \quad (\text{claim}) \\
  H_a: \mu < 860
  \]

**Part (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.)

- **Option A**: The critical values are \(\_\).

- **Option B**: The critical value is \(\_\).

*Explanation:*
This section allows you to calculate the critical value for a one-tailed test using a standard normal distribution, given a significance level of 0.10. Use statistical software or a z-table to find this value.
Transcribed Image Text:**Hypothesis Testing of Mean Monthly Residential Electricity Consumption** A company claims that the mean monthly residential electricity consumption in a certain region is more than 860 kilowatt-hours (kWh). You want to test this claim. You find that a random sample of 66 residential customers has a mean monthly consumption of 900 kWh. Assume the population standard deviation is 123 kWh. At a significance level (\(\alpha\)) of 0.10, can you support the claim? Complete parts (a) through (e). --- **Part (a):** Define the null and alternative hypotheses: - **Option A**: \[ H_0: \mu \neq 860 \quad (\text{claim}) \\ H_a: \mu \neq 860 \] - **Option B**: \[ H_0: \mu \geq 900 \quad (\text{claim}) \\ H_a: \mu < 900 \] - **Option C**: \[ H_0: \mu \neq 900 \\ H_a: \mu \neq 900 \quad (\text{claim}) \] - **Option D**: \[ H_0: \mu \leq 860 \\ H_a: \mu > 860 \quad (\text{claim}) \quad \text{(Selected)} \] - **Option E**: \[ H_0: \mu \geq 860 \quad (\text{claim}) \\ H_a: \mu < 860 \] **Part (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.) - **Option A**: The critical values are \(\_\). - **Option B**: The critical value is \(\_\). *Explanation:* This section allows you to calculate the critical value for a one-tailed test using a standard normal distribution, given a significance level of 0.10. Use statistical software or a z-table to find this value.
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