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.)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1f7037f-b2ab-43a0-aa28-3207bbcdb8a6%2F343b1bfc-6384-425f-b645-83c04f3553f2%2F5mu9z7_processed.jpeg&w=3840&q=75)
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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