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 of25similar vehicles has a mean price of$19,675and a standard deviation of$1992.Is there enough evidence to reject the claim atα=0.01?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 arandom sample of 25 similar vehicles has a mean price of $19,675 and a standard deviation of $1992. Is there enough evidence to reject the claim ata = 0.01? Complete parts (a) through (e) below. Assume the population is normally distributed.(a) Write the claim mathematically and identify Ho and Ha.Which of the following correctly states H, and Ha?OC. Ho: H = $19,000Ο Α. H : μ > $19,000H3:us $19,000Ο Β. Η0: μ= $19,000Hạ:u> $19,000Ha: µ< $19,000Ο D . Hρ: μ = $19,000Ha: u = $19,000OF. Ho: H = $19,000Haiu = $19,000O E. Ho: H2 $19,000H3i H< $19,000(b) Find the critical value(s) and identify the rejection region(s).What is(are) the critical value(s), to?to =O(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.O B. t<O D. t>(c) Find the standardized test statistic t.(Round to two decimal places as needed.)t3D(d) Decide whether to reject or fail to reject the null hypothesis.O A. Fail to reject H, because the test statistic is in the rejection region(s).O B. Reject H, because the test statistic is in the rejection region(s)OC. Reject Ho because the test statistic is not in the rejection region(s).O D. Fail to reject H, because the test statistic is not 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 sufficient evidence to reject the claim that the mean price is not $19,00.O B. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is not $19,000.OC. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean price is $19,000.O D. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is $19,000.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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

similar vehicles has a mean price of

$19,675

and a standard deviation of

$1992.

Is there enough evidence to reject the claim at

α=0.01?

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 $19,675 and a standard deviation of $1992. Is there enough evidence to reject the claim at
a = 0.01? Complete parts (a) through (e) below. Assume the population is normally distributed.
(a) Write the claim mathematically and identify Ho and Ha.
Which of the following correctly states H, and Ha?
OC. Ho: H = $19,000
Ο Α. H : μ > $19,000
H3:us $19,000
Ο Β. Η0: μ= $19,000
Hạ:u> $19,000
Ha: µ< $19,000
Ο D . Hρ: μ = $19,000
Ha: u = $19,000
OF. Ho: H = $19,000
Haiu = $19,000
O E. Ho: H2 $19,000
H3i H< $19,000
(b) Find the critical value(s) and identify the rejection region(s).
What is(are) the critical value(s), to?
to =O
(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.
O B. t<
<t<
O C. t<
and t>
O D. t>
(c) Find the standardized test statistic t.
(Round to two decimal places as needed.)
t3D
(d) Decide whether to reject or fail to reject the null hypothesis.
O A. Fail to reject H, because the test statistic is in the rejection region(s).
O B. Reject H, because the test statistic is in the rejection region(s)
OC. Reject Ho because the test statistic is not in the rejection region(s).
O D. Fail to reject H, because the test statistic is not 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 sufficient evidence to reject the claim that the mean price is not $19,00.
O B. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is not $19,000.
OC. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean price is $19,000.
O D. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is $19,000.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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