**Hypothesis Testing Example: Used Car Dealer's Claim****Scenario:**A used car dealer states that the mean price of a three-year-old sports utility vehicle (SUV) is $19,000. There is suspicion regarding the validity of this claim. A random sample of 25 similar vehicles shows a mean price of $19,648 with a standard deviation of $1915. The goal is to determine if there is enough evidence to reject the dealer’s claim at a significance level of $\alpha = 0.10$. The assumption is that the population is normally distributed.**Steps to Follow:**(a) **Determine the Rejection Region(s):**You need to select the correct rejection region(s) and fill in the answer box(es) within your choice. This should be done by rounding to three decimal places as needed.Options:- A. $ \square < t < \square $- B. $ t > \square $- C. $ t < \square $ and $ t > \square $- D. $ t < \square $(b) **Find the Standardized Test Statistic $t$:**The formula for the standardized test statistic $t$ is:\[ t = \frac{\bar{X} - \mu}{s / \sqrt{n}} \]Where,- $\bar{X} = 19,648$ (sample mean)- $\mu = 19,000$ (population mean)- $s = 1915$ (sample standard deviation)- $n = 25$ (sample size)You need to round the calculated $t$-value to two decimal places as needed.(c) **Decide whether to reject or fail to reject the null hypothesis $H_{0}$:**Options:- A. Reject $ H_0 $ because the test statistic is not in the rejection region(s).- B. Fail to reject $ H_0 $ because the test statistic is in the rejection region(s).Click to select your answer(s).---**Graphical or Diagram Explanation (if present):**No graphs or diagrams are provided in the image. The explanation involves understanding hypothesis testing steps and the decision-making process upon obtaining the $ t $-test results.This process is important for evaluating claims statistically to make informed decisions based on sample data. ### Hypothesis Testing ExampleA used car dealer claims that the mean price of a three-year-old sports utility vehicle (SUV) is $19,000. You suspect this claim is incorrect and find that a random sample of 25 similar vehicles has a mean price of $19,648 and a standard deviation of $1915. Is there enough evidence to reject the claim at a 0.10 significance level? Complete parts (a) through (e) 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 = \$19,000 $ - $ H_a: \mu \neq \$19,000 $ - **B.** - $ H_0: \mu \neq \$19,000 $ - $ H_a: \mu = \$19,000 $ - **C.** - $ H_0: \mu \geq \$19,000 $ - $ H_a: \mu < \$19,000 $ - **D.** - $ H_0: \mu = \$19,000 $ - $ H_a: \mu > \$19,000 $ - **E.** - $ H_0: \mu > \$19,000 $ - $ H_a: \mu \leq \$19,000 $ - **F.** - $ H_0: \mu = \$19,000 $ - $ H_a: \mu < \$19,000 $#### (b) Find the critical value(s) and identify the rejection region(s).*What is/are the critical value(s), $ t_0 $?*- $ t_0 = $ ______*Use a comma to separate answers as needed. Round to three decimal places as needed.*

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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 25 similar vehicles has a mean price of $19,648 and a standard deviation of $1915. 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 25 similar vehicles has a mean price of $19,648 and a standard deviation of $1915. 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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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