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$19,623and a standard deviation of$1950.Is there enough evidence to reject the claim atα=0.05?Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Write the claim mathematically and identifyH0andHa. Which of the following correctly statesH0andHa? A.H0:μ=$19,000Ha:μ>$19,000 B.H0:μ=$19,000Ha:μ≠$19,000 C.H0:μ≠$19,000Ha:μ=$19,000 D.H0:μ>$19,000Ha:μ≤$19,000 E.H0:μ≥$19,000Ha:μ<$19,000 F.H0:μ=$19,000Ha:μ<$19,000(b) Find the critical value(s) and identify the rejection region(s). What is(are) the critical value(s),t0? t0=enter your response here(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.enter your response here<t<enter your response here B.t<enter your response hereandt>enter your response here C.t<enter your response here D.t>enter your response here(c) Find the standardized test statistic t. t=enter your response here(Round to two decimal places as needed.)(d) Decide whether to reject or fail to reject the null hypothesis. A.RejectH0because the test statisticisin the rejection region(s). B.Fail to rejectH0because the test statisticisin the rejection region(s). C.RejectH0because the test statisticis notin the rejection region(s). D.Fail to rejectH0because the test statisticis notin the rejection region(s).(e) Interpret the decision in the context of the original claim. A.At the5%level of significance, thereis notsufficient evidence to reject the claim that the mean price is $19,000. B.At the5%level of significance, thereis notsufficient evidence to reject the claim that the mean price is not $19,000. C.At the5%level of significance, thereissufficient evidence to reject the claim that the mean price is $19,000. D.At the5%level of significance, thereissufficient evidence to reject the claim that the mean price is not $19,000. TextbookCalculator

Given : Claim : The mean price is $19,000.

Answered: used car dealer says that the mean…

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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Question

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

$19,623

and a standard deviation of

$1950.

Is there enough evidence to reject the claim at

α=0.05?

Complete parts (a) through (e) below. Assume the population is normally distributed.

(a) Write the claim mathematically and identify

and

Ha.

Which of the following correctly states

and

Ha?

H0:

μ=$19,000

Ha:

μ>$19,000

H0:

μ=$19,000

Ha:

μ≠$19,000

H0:

μ≠$19,000

Ha:

μ=$19,000

H0:

μ>$19,000

Ha:

μ≤$19,000

H0:

μ≥$19,000

Ha:

μ<$19,000

H0:

μ=$19,000

Ha:

μ<$19,000

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

What is(are) the critical value(s),

t0?

t0=enter your response here

(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.)

enter your response here<t<enter your response here

t<enter your response here

and

t>enter your response here

t<enter your response here

t>enter your response here

t=enter your response here

(Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

Reject

because the test statistic

in the rejection region(s).

Fail to reject

because the test statistic

in the rejection region(s).

Reject

because the test statistic

is not

in the rejection region(s).

Fail to reject

because the test statistic

is not

in the rejection region(s).

(e) Interpret the decision in the context of the original claim.

At the

level of significance, there

is not

sufficient evidence to reject the claim that the mean price is $19,000.

At the

level of significance, there

is not

sufficient evidence to reject the claim that the mean price is not $19,000.

At the

level of significance, there

sufficient evidence to reject the claim that the mean price is $19,000.

At the

level of significance, there

sufficient evidence to reject the claim that the mean price is not $19,000.

TextbookCalculator

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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