Question

14. Consider the following ANOVA table, the null hypothesis for this ANOVA problem is Source of Variation SS DF MS F Between ? 3 ? 3 Within ? ? 20 Total ? 18 (A) H0: ?1 = ?2 (B) H0: ?1 = ?2 = ?3 (C) H0: ?1 = ?2 = ?3 = ?4 (D) None of the above. 15. Refer to above problem, The total sum of squares (SSTO) is (A) 80. (B) 180. (C) 300 (D) 480 16. Refer to above problem, The variance between samples is (A) 20. (B) 60 (C) 180 (D) 300 (E) 480 17. Refer to above problem, the value of the test statistics is (A) 15 (B) 12 (C) 4 (D) 3 18. Refer to above problem, at ? = 0.05, the critical value is (A) 3.06 (B) 3.29 (C) 4.15 (D) 8.70 (E) ???? 19. Refer to above problem, the p-value is (A) greater than 0.10 (B) between 0.05 to 0.10 (C) less than 0.05 (D) None of the above 20. Refer to above problem, at ? = 0.1 ?, we conclude that A. Reject H0, there is enough evidence to conclude that there is a difference in the population mean. B. Reject H0, there is not significant difference between the four population means. C. Fail to reject H0, there is not significant difference between the four population means. D. None of the above.

          14. Consider the following ANOVA table, the null hypothesis for this ANOVA problem is
Source of Variation SS DF MS F
Between ? 3 ? 3
Within ? ? 20
Total ? 18
(A) H0: ?1 = ?2 (B) H0: ?1 = ?2 = ?3 (C) H0: ?1 = ?2 = ?3 = ?4 (D) None of the above.
15. Refer to above problem, The total sum of squares (SSTO) is
(A) 80. (B) 180. (C) 300 (D) 480
16. Refer to above problem, The variance between samples is
(A) 20. (B) 60 (C) 180 (D) 300 (E) 480
17. Refer to above problem, the value of the test statistics is
(A) 15 (B) 12 (C) 4 (D) 3
18. Refer to above problem, at ? = 0.05, the critical value is
(A) 3.06 (B) 3.29 (C) 4.15 (D) 8.70 (E) ????
19. Refer to above problem, the p-value is
(A) greater than 0.10 (B) between 0.05 to 0.10 (C) less than 0.05 (D) None of the above
20. Refer to above problem, at ? = 0.1 ?, we conclude that
A. Reject H0, there is enough evidence to conclude that there is a difference in the population mean.
B. Reject H0, there is not significant difference between the four population means.
C. Fail to reject H0, there is not significant difference between the four population means.
D. None of the above.

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14. Consider the following ANOVA table, the null hypothesis for this ANOVA problem is
Source of Variation SS DF MS F
Between ? 3 ? 3
Within ? ? 20
Total ? 18
(A) H0: ?1 = ?2 (B) H0: ?1 = ?2 = ?3 (C) H0: ?1 = ?2 = ?3 = ?4 (D) None of the above.
15. Refer to above problem, The total sum of squares (SSTO) is
(A) 80. (B) 180. (C) 300 (D) 480
16. Refer to above problem, The variance between samples is
(A) 20. (B) 60 (C) 180 (D) 300 (E) 480
17. Refer to above problem, the value of the test statistics is
(A) 15 (B) 12 (C) 4 (D) 3
18. Refer to above problem, at ? = 0.05, the critical value is
(A) 3.06 (B) 3.29 (C) 4.15 (D) 8.70 (E) ????
19. Refer to above problem, the p-value is
(A) greater than 0.10 (B) between 0.05 to 0.10 (C) less than 0.05 (D) None of the above
20. Refer to above problem, at ? = 0.1 ?, we conclude that
A. Reject H0, there is enough evidence to conclude that there is a difference in the population mean.
B. Reject H0, there is not significant difference between the four population means.
C. Fail to reject H0, there is not significant difference between the four population means.
D. None of the above.

Added by Anthony B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Qudsiya Anis

09/30/2023

Step 1

From the given options, the correct null hypothesis is: (A) $H_0: \mu_1 = \mu_2 = \mu_3$ Now, let's find the total sum of squares (SSTO). From the given options, the correct answer is: (B) SSTO = 180 Show more…

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14. Consider the following ANOVA table, the null hypothesis for this ANOVA problem is Source of Variation SS DF MS F Between ? 3 ? 3 Within ? ? 20 Total ? 18 (A) H0: μ1 = μ2 (B) H0: μ1 = μ2 = μ3 (C) H0: μ1 = μ2 = μ3 = μ4 (D) None of the above. 15. Refer to above problem, The total sum of squares (SSTO) is (A) 80. (B) 180. (C) 300 (D) 480 16. Refer to above problem, The variance between samples is (A) 20. (B) 60 (C) 180 (D) 300 (E) 480 17. Refer to above problem, the value of the test statistics is (A) 15 (B) 12 (C) 4 (D) 3 18. Refer to above problem, at α = 0.05, the critical value is (A) 3.06 (B) 3.29 (C) 4.15 (D) 8.70 (E) 以上皆非 19. Refer to above problem, the p-value is (A) greater than 0.10 (B) between 0.05 to 0.10 (C) less than 0.05 (D) None of the above 20. Refer to above problem, at α = 0.1, we conclude that A. Reject H0, there is enough evidence to conclude that there is a difference in the population mean. B. Reject H0, there is not significant difference between the four population means. C. Fail to reject H0, there is not significant difference between the four population means. D. None of the above.

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Transcript

00:01 So, in the given question, we have been provided an anova table and on the basis of that we have been asked that what will be the null hypothesis here.

00:09 Now here, the degrees of freedom between this is equal to 3, right.

00:15 So here, k -1 is equal to 3, so the value of k is 4, right.

00:21 So the number of groups here is 4, so our null hypothesis will be that the mean of the 4 populations is equal, right.

00:32 So the correct option for the first is option c.

00:36 Now the next question is that what is the total sum of squares, okay.

00:41 So in this case, the degrees of freedom within will be equal to n -k -1 that is equal to 18 -3 that is 15.

00:52 Now the sum of square within this is 20 multiplied by 15 that is 300, the mean sum of square between this is 20 into 3 that is 60, so the sum of square between will be 60 into 3 that is 180, right.

01:10 So here, the sum of square total will be equal to 300 plus 180 that is 480, right.

01:18 So for this, the correct option for this one is option d.

01:23 Now the next is here, it says that what is the variance between the samples here, okay.

01:31 So here, the variance between the sample, this is equal to the mean sum square between which is equal to 20 into 3 that is equal to 60, alright.

01:44 So for this, the correct option for this one will be, this is equal to option b, right.

01:52 Now in the next part, it says that what is the value of the test statistics...

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