A sporting goods store believes the average age of its customers is 37 or less. A random sample of 45 customers was surveyed, and the average customer age wa found to be 40.3 years. Assume the standard deviation for customer age is 9.0 years. Using a =0.10, complete parts a and b below. a. Does the sample provide enough evidence to refute the age claim made by the sporting goods store? Determine the null and alternative hypotheses. Ho: H:H The z-test statistic is (Round to two decimal places as needed.)

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**Statistical Hypothesis Testing Example**

A sporting goods store believes the average age of its customers is 37 or less. A random sample of 45 customers was surveyed, and the average customer age was found to be 40.3 years. Assume the standard deviation for customer age is 9.0 years. Using α = 0.10, complete the following tasks:

### a. Test the Age Claim

Does the sample provide enough evidence to refute the age claim made by the sporting goods store?

**Step 1: Determine Hypotheses**

- **Null Hypothesis (H₀):** The average age of customers (μ) is 37 years or less.
- **Alternative Hypothesis (H₁):** The average age of customers (μ) is greater than 37 years.

**Step 2: Calculate Test Statistic**

Find the z-test statistic. (Round to two decimal places as needed.)

**Step 3: Identify Critical Z-Score(s)**

Determine the critical z-score(s). (Round to two decimal places as needed. Use a comma to separate answers as needed.)

**Step 4: Decision**

Based on the test statistic, decide whether to reject or fail to reject the null hypothesis. 

### b. Determine the p-value for this test

Find the p-value. (Round to three decimal places as needed.)

**Enter your answer in the provided answer boxes.**

---

Note: This example is for educational purposes, demonstrating the process of hypothesis testing using z-scores and p-values.
Transcribed Image Text:**Statistical Hypothesis Testing Example** A sporting goods store believes the average age of its customers is 37 or less. A random sample of 45 customers was surveyed, and the average customer age was found to be 40.3 years. Assume the standard deviation for customer age is 9.0 years. Using α = 0.10, complete the following tasks: ### a. Test the Age Claim Does the sample provide enough evidence to refute the age claim made by the sporting goods store? **Step 1: Determine Hypotheses** - **Null Hypothesis (H₀):** The average age of customers (μ) is 37 years or less. - **Alternative Hypothesis (H₁):** The average age of customers (μ) is greater than 37 years. **Step 2: Calculate Test Statistic** Find the z-test statistic. (Round to two decimal places as needed.) **Step 3: Identify Critical Z-Score(s)** Determine the critical z-score(s). (Round to two decimal places as needed. Use a comma to separate answers as needed.) **Step 4: Decision** Based on the test statistic, decide whether to reject or fail to reject the null hypothesis. ### b. Determine the p-value for this test Find the p-value. (Round to three decimal places as needed.) **Enter your answer in the provided answer boxes.** --- Note: This example is for educational purposes, demonstrating the process of hypothesis testing using z-scores and p-values.
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