Question

Each student in a section of business statistics provided his/her 5 favorite movies, along with the IMDB score (1-10) and Gross receipts (at that point in time and not corrected for inflation). The IMDB score was used to identify the “Good Movies” (IMDB score must be above 8).

            Is there a difference in Gross Receipts between Good Action movies and Good Drama movies? The following output was created at alpha = 0.05.

t-Test: Two-Sample Assuming Unequal Variances

Good Action	Good Drama
Mean	Good Action    240,003,897.44	Good Drama 75,085,009.71
Variance	6.31578E+16	2.6366E+15
Observations	9	7
Hypothesized Mean Difference	0
Df	9
t Stat	1.918
P(T<=t) one-tail	0.044
t Critical one-tail	1.833
P(T<=t) two-tail	0.087
t Critical two-tail	2.262

What is the calculated value of the appropriate test statistic to test the belief at the 5% level of significance that there is no difference in average Gross Receipts between Good Action and Good Drama movies?

a) 0.087

b) 0.044

c) 2.262

d) 1.918

What are the decision and conclusion of the test at alpha = 0.05?

a) Fail to reject the null hypothesis, conclude there is insufficient evidence of a difference in gross receipts between Good Action and Good Drama, on average.

b) Reject the null hypothesis, conclude there is insufficient evidence of a difference in gross receipts between Good Action and Good Drama, on average.

c) Fail to reject the null hypothesis, conclude there is sufficient evidence of a difference in gross receipts between Good Action and Good Drama, on average.

d) Reject the null hypothesis, conclude there is sufficient evidence of a difference in gross receipts between Good Action and Good Drama, on average.

What assumption does this test rely upon?

a) not the answer

b) equality of variances

c) large sample sizes

d) normality of gross receipts

Answer 1

a) The calculated value of the appropriate test statistic to test the belief at the 5% level of significance that there is no difference in average Gross Receipts between Good Action and Good Drama movies is 1.918.

Hence option d is the correct answer.

b) The two tailed critical value of t is 2.262.

The calculated value of t is 1.918.

Since the calculated value of t is 1.918 which is less than tabulated value of 2.262, hence the null hypothesis is accepted and we conclude that there is no difference in gross receipts between Good Action and Good Drama, on average.

Fail to reject the null hypothesis, conclude there is insufficient evidence of a difference in gross receipts between Good Action and Good Drama, on average.

Hence option a is the correct answer.

c) The normality of population is assumed for testing that is normality of gross receipts.

Hence option d is the correct answer.