Homework Help is Here – Start Your Trial Now!
Math
Statistics
A used car dealer says that the mean price of a three-year-old sports utility vehicle is $19,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $19,826 and a standard deviation of $1935. Is there enough evidence to reject the claim at a=0.10? Complete parts (a) through (e) below. Assume the population is normally distributed.

A used car dealer says that the mean price of a three-year-old sports utility vehicle is $19,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $19,826 and a standard deviation of $1935. Is there enough evidence to reject the claim at a=0.10? Complete parts (a) through (e) below. Assume the population is normally distributed.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

Answer the question 

### Hypothesis Testing Example: Mean Price of Used SUVs #### Scenario: A used car dealer claims that the mean price of a three-year-old sports utility vehicle (SUV) is $19,000. You believe this claim is incorrect. You conduct a study involving a random sample of 22 similar vehicles and find that the mean price is $19,826 with a standard deviation of $1935. You want to determine if there is enough evidence to reject the dealer’s claim at a significance level of \(\alpha = 0.10\). Assume the population is normally distributed. ### Step-by-Step Solution: #### Part (a): State the Hypotheses You need to determine the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)). The hypotheses options provided are: - **Option A:** - \(H_0: \mu = \$19,000\) - \(H_a: \mu > \$19,000\) - **Option B:** - \(H_0: \mu = \$19,000\) - \(H_a: \mu < \$19,000\) - **Option C:** - \(H_0: \mu \geq \$19,000\) - \(H_a: \mu < \$19,000\) - **Option D:** - \(H_0: \mu = \$19,000\) - \(H_a: \mu \neq \$19,000\) - **Option E:** - \(H_0: \mu \leq \$19,000\) - \(H_a: \mu > \$19,000\) - **Option F:** - \(H_0: \mu > \$19,000\) - \(H_a: \mu \leq \$19,000\) **Correct Hypotheses:** - \(H_0: \mu = \$19,000\) - \(H_a: \mu \neq \$19,000\) This indicates a two-tailed test. #### Part (b): Find the Critical Value(s) and Identify the Rejection Region(s) You need to determine the critical value (\(t_0\)) for a two-tailed test with \(\alpha = 0.10\). To find the critical values
Transcribed Image Text:### Hypothesis Testing Example: Mean Price of Used SUVs #### Scenario: A used car dealer claims that the mean price of a three-year-old sports utility vehicle (SUV) is $19,000. You believe this claim is incorrect. You conduct a study involving a random sample of 22 similar vehicles and find that the mean price is $19,826 with a standard deviation of $1935. You want to determine if there is enough evidence to reject the dealer’s claim at a significance level of \(\alpha = 0.10\). Assume the population is normally distributed. ### Step-by-Step Solution: #### Part (a): State the Hypotheses You need to determine the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)). The hypotheses options provided are: - **Option A:** - \(H_0: \mu = \$19,000\) - \(H_a: \mu > \$19,000\) - **Option B:** - \(H_0: \mu = \$19,000\) - \(H_a: \mu < \$19,000\) - **Option C:** - \(H_0: \mu \geq \$19,000\) - \(H_a: \mu < \$19,000\) - **Option D:** - \(H_0: \mu = \$19,000\) - \(H_a: \mu \neq \$19,000\) - **Option E:** - \(H_0: \mu \leq \$19,000\) - \(H_a: \mu > \$19,000\) - **Option F:** - \(H_0: \mu > \$19,000\) - \(H_a: \mu \leq \$19,000\) **Correct Hypotheses:** - \(H_0: \mu = \$19,000\) - \(H_a: \mu \neq \$19,000\) This indicates a two-tailed test. #### Part (b): Find the Critical Value(s) and Identify the Rejection Region(s) You need to determine the critical value (\(t_0\)) for a two-tailed test with \(\alpha = 0.10\). To find the critical values
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS