Question

Under specified driving conditions, an automobile manufacturer believes that its new SUV will get more miles per gallon (mpg) than other automobiles in its class. For automobiles of the same class, the mean is 22 with a variance of 16.00 mpg. To investigate, the manufacturer tested 25 of its new SUV in which the mean was 20.5 mpg. What can be concluded with α = 0.01?

a) What is the appropriate test statistic?
---Select---naz-testone-sample t-testindependent-samples t-testrelated-samples t-test

b)
Population:
---Select---SUVs in same classmpgspecified conditionsautomobile manufacturertested SUVs
Sample:
---Select---SUVs in same classmpgspecified conditionsautomobile manufacturertested SUVs

c) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =______ ; test statistic = _________
Decision: ---Select---Reject H0Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[____ , _____ ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and select "na" below.
d =_______ ;  ---Select---natrivial effectsmall effectmedium effectlarge effect
r² =____ ;  ---Select---natrivial effectsmall effectmedium effectlarge effect

f) Make an interpretation based on the results.

Under the specified conditions, the new SUV gets significantly more mpg than other automobiles in its class.

Under the specified conditions, the new SUV gets significantly less mpg than other automobiles in its class.    

Under the specified conditions, the new SUV does not get significantly different mpg than other automobiles in its class.

Answer 1

a)

Answer:

z-test

Explanation:

Since we are comparing the one sample mean with the hypothesized population mean and the population standard deviation is known, the one-sample z test will be used.

b)

Answer:

Population: SUVs in the same class

Sample: automobile manufacturer tested SUVs

Explanation:

The population represents the complete set of data values while the sample represents the subset of a population. In this scenario, the manufacturer wants to compare the mileage of its new SUV with the other SUVs which means the all the other represents a population and the new SUV represents a sample such that the manufacturer wants to test whether the sample are from the same population or different.

c)

Answer:

critical value = 2.3263;

test statistic = -1.875

Decision: Fail to reject H0

Explanation:

Hypothesis

The Null and Alternative Hypotheses are,

This is a right-tailed test

Critical value

The critical value for the z statistic is obtained from the standard normal distribution table for significance level = 0.01 for the right-tailed test.

Test statistic

Decision

Since the z statistic is less than critical value, the null hypothesis is not rejected.

d)

Answer:

Explanation:

The confidence interval for the mean is obtained using the formula,

e)

Answer:

d = 0.375; small effect

r^2 = na

Explanation:

The effect size, Cohen's d is obtained using the following formula,

(absolute value is taken, ignore the -ve sign)

d = 0.375 which means, the sample mean is 0.375 standard deviation away from the population mean which is not large hence the effect is small

The effect size r^2 is defined for the two-sample test

f)

Answer:

Under the specified conditions, the new SUV does not get significantly different mpg than other automobiles in its class.

Explanation:

The result from the hypothesis says that the null hypothesis is not rejected hence the result can be concluded as, there is not sufficient evidence to conclude that the new SUV is will get more miles per gallon (mpg) than other automobiles in its class which means the new SUV does not get significantly different mpg than other automobiles in its class.