Aused car dealer says that the mean price of a three-year-old sports utility vehicle is $23,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of 523,691 and a standard deviation of $1911. Is there enough evidence to reject the claim at a=0.01? Complete parts (a) through (e) below. Assume the population is normally distributed. U N du (c) Find the standardized test statistic t t=D (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. O A. Fail to reject Ho because the test statistic is in the rejection region(s). O B. Reject Ho because the test statistic is not in the rejection region(s). OC. Fail to reject Ho because the test statistic is not in the rejection region(s). O D. Reject H, because the test statistic is in the rejection region(s). (e) Interpret the decision in the context of the original claim O A. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is not $23,000. O B. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean price is $23,000 O C. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is $23,000. O D. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean price is not $23,000. Next

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Question
Answer all questions A-E
The image shows a statistics problem involving hypothesis testing.

**Problem Statement:**
A used car dealer claims that the mean price of a three-year-old sports utility vehicle (SUV) is $23,000. You suspect this claim is incorrect and conduct a test, finding that a random sample of 22 similar vehicles has a mean price of $23,691 and a standard deviation of $1911. You want to determine if there is enough evidence to reject the dealer’s claim at the 0.01 significance level (α = 0.01). Assume the population is normally distributed.

**Tasks:**
- **(c) Find the standardized test statistic t:**
  - Use the sample mean, population mean, sample standard deviation, and sample size to calculate the t-statistic.
  - Round the t-statistic to two decimal places.

- **(d) Decide whether to reject or fail to reject the null hypothesis:**
  - A. Fail to reject H₀ because the test statistic is in the rejection region(s).
  - B. Reject H₀ because the test statistic is not in the rejection region(s).
  - C. Fail to reject H₀ because the test statistic is not in the rejection region(s).
  - D. Reject H₀ because the test statistic is in the rejection region(s).

- **(e) Interpret the decision in the context of the original claim:**
  - A. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is not $23,000.
  - B. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean price is $23,000.
  - C. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is $23,000.
  - D. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean price is not $23,000.

**Note:**
The highlighted options in sections (d) and (e) indicate the selected answers. In section (d), option A is selected, and in section (e), option C is selected.
Transcribed Image Text:The image shows a statistics problem involving hypothesis testing. **Problem Statement:** A used car dealer claims that the mean price of a three-year-old sports utility vehicle (SUV) is $23,000. You suspect this claim is incorrect and conduct a test, finding that a random sample of 22 similar vehicles has a mean price of $23,691 and a standard deviation of $1911. You want to determine if there is enough evidence to reject the dealer’s claim at the 0.01 significance level (α = 0.01). Assume the population is normally distributed. **Tasks:** - **(c) Find the standardized test statistic t:** - Use the sample mean, population mean, sample standard deviation, and sample size to calculate the t-statistic. - Round the t-statistic to two decimal places. - **(d) Decide whether to reject or fail to reject the null hypothesis:** - A. Fail to reject H₀ because the test statistic is in the rejection region(s). - B. Reject H₀ because the test statistic is not in the rejection region(s). - C. Fail to reject H₀ because the test statistic is not in the rejection region(s). - D. Reject H₀ because the test statistic is in the rejection region(s). - **(e) Interpret the decision in the context of the original claim:** - A. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is not $23,000. - B. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean price is $23,000. - C. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is $23,000. - D. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean price is not $23,000. **Note:** The highlighted options in sections (d) and (e) indicate the selected answers. In section (d), option A is selected, and in section (e), option C is selected.
## Hypothesis Testing Exercise

A used car dealer claims that the mean price of a three-year-old sports utility vehicle is $23,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $23,691 and a standard deviation of $1911. Is there enough evidence to reject the claim at α = 0.01? Complete parts (a) through (c) below. Assume the population is normally distributed.

### (a) Write the claim mathematically and identify \( H_0 \) and \( H_a \).

Which of the following correctly states \( H_0 \) and \( H_a \)?

- **A.** \( H_0: \mu = \$23,000 \)  
  \( H_a: \mu < \$23,000 \)
  
- **B.** \( H_0: \mu = \$23,000 \)  
  \( H_a: \mu > \$23,000 \)

- **C.** \( H_0: \mu \neq \$23,000 \)  
  \( H_a: \mu = \$23,000 \)

- **D.** \( H_0: \mu = \$23,000 \)  
  \( H_a: \mu \neq \$23,000 \)

- **E.** \( H_0: \mu \neq \$23,000 \)  
  \( H_a: \mu > \$23,000 \)

- **F.** \( H_0: \mu \geq \$23,000 \)  
  \( H_a: \mu < \$23,000 \)

### (b) Find the critical value(s) and identify the rejection region(s).

What is(are) the critical value(s), \( t_0 \)?  
(Use a comma to separate answers as needed. Round to three decimal places as needed.)

Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice.  
(Round to three decimal places as needed.)

- **A.** \( t < \_\_\_ \)

- **B.** \( t > \_\_\_ \)

- **C.** \( t < \_\_\_ \) and \( t > \_\_\_ \)

- **D.** \( t < \_\_\_ \)
Transcribed Image Text:## Hypothesis Testing Exercise A used car dealer claims that the mean price of a three-year-old sports utility vehicle is $23,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $23,691 and a standard deviation of $1911. Is there enough evidence to reject the claim at α = 0.01? Complete parts (a) through (c) below. Assume the population is normally distributed. ### (a) Write the claim mathematically and identify \( H_0 \) and \( H_a \). Which of the following correctly states \( H_0 \) and \( H_a \)? - **A.** \( H_0: \mu = \$23,000 \) \( H_a: \mu < \$23,000 \) - **B.** \( H_0: \mu = \$23,000 \) \( H_a: \mu > \$23,000 \) - **C.** \( H_0: \mu \neq \$23,000 \) \( H_a: \mu = \$23,000 \) - **D.** \( H_0: \mu = \$23,000 \) \( H_a: \mu \neq \$23,000 \) - **E.** \( H_0: \mu \neq \$23,000 \) \( H_a: \mu > \$23,000 \) - **F.** \( H_0: \mu \geq \$23,000 \) \( H_a: \mu < \$23,000 \) ### (b) Find the critical value(s) and identify the rejection region(s). What is(are) the critical value(s), \( t_0 \)? (Use a comma to separate answers as needed. Round to three decimal places as needed.) Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.) - **A.** \( t < \_\_\_ \) - **B.** \( t > \_\_\_ \) - **C.** \( t < \_\_\_ \) and \( t > \_\_\_ \) - **D.** \( t < \_\_\_ \)
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