Question

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question 24) Find the critical value. 24) Source DF SS MS F P treatments 3 13.500 4.500 5.17 0.011 16 13.925 0.870 19 27.425 Total C) 3.06 A) 8.70 B) 3.24 D) 5.42 25) What can you conclude about the equality of the population means? Use level of significance of 25) 0.05 SourceDF SS MS F treatments 3 13.500 4.500 5.17 0011 16 13.925 0.870 Total A) Accept the null hypothesis since the p-value is greater than the significance level. B) Accept the null hypothesis since the p-value is less than the significance level C) Reject the null hypothesis since the p-value is less than the significance level D) Reject the null hypothesis since the p-value is greater than the significance level 19 27.425 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. 26) At the 0.025 significance level, test the claim that the three brands have the same mean if 26) the following sample results have been obtained. Brand A Brand B Brand C 27 24 37 33 32 30 32 25 22 21 36

Answer 1

(24)

Correct option:

(B)    3.24

Explanation: For degrees of freedom for numerator = 3 and degrees of freedom for denominator = 16, Table gives critical value of F = 3.24

(25)

Correct option:

(c) Reject the null hypothesis since the p - value is less than the significance level.

(26)

Correct option:

The data do not support the claim that the three brands have the same mean.

Explanation:

From the given data, ANOVA Table is calculated as follows:

Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F - Stat	P - Value
Between Groups	2	325.3688	325.3688/2=162.6844	162.6844/13.4195=12.123	0.0013
Within Groups	12	161.0343	161.0343/12=13.4195
Total	14	486.4031

Since P - value = 0.0013 is less than $\alpha$ = 0.025, the difference is significant. Reject null hypothesis.

Conclusion:

The data do not support the claim that the three brands have the same mean.