samples of four different models of cars were selected and the gas mileage of ea

Question

samples of four different models of cars were selected and the gas mileage of each car was measured. The results are shown below.
model A -- model B -- model C -- model D

23 -- 28 -- 30 -- 25

25 -- 26 -- 28 -- 26

24 -- 29 -- 32 -- 25

26 -- 30 -- 27 -- 35
Test the claim that the four different models have the same population mean.

1. Referring to Scenario 3, the observed value of the test statistic is:

D. 3.49

2. Referring to Scenario 3, the critical value of the test statistic is:

D. 0.16

3. Referring to Scenario 3, the p value is:

D. 2.04

4. Referring to Scenario 3, the Sum of Squares (between groups) is:

D. None of the other choices is correct

5. Referring to Scenario 3, the decision is:

D. Reject null hypothesis, means are not different

A. None of the other choices is correct B. 2.04 C. 0.16

D. 3.49

2. Referring to Scenario 3, the critical value of the test statistic is:

A. None of the other choices is correct B. 2.04 C. 3.49

D. 0.16

3. Referring to Scenario 3, the p value is:

A. 0.16 B. 3.49 C. None of the other choices is correct

D. 2.04

4. Referring to Scenario 3, the Sum of Squares (between groups) is:

A. 99.25 B. 16.90 C. 50.69

D. None of the other choices is correct

5. Referring to Scenario 3, the decision is:

A. None of the other choices is correct B. Reject null hypothesis, means are different C. Fail to reject null hypothesis, means are not different

D. Reject null hypothesis, means are not different

Explanation / Answer

Below are the results of ANOVA analysis conducted using given data in the question

(1)
Value of test statistics F = 2.04 (option B)

(2)
Critical value of the test statistics Fcrit = 3.49 (option C)

(3)
p-value = 0.16 (option A)

(4)
Sum of squares (between groups) = 50.69 (option C)

(5)
As p-value is greater than the significance level of 0.05, we fail to reject null hypothesis.
C. Fail to reject null hypothesis, means are not different

SUMMARY Groups Count Sum Average Variance A 4 98 24.5 1.666667 B 4 113 28.25 2.916667 C 4 117 29.25 4.916667 D 4 111 27.75 23.58333

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