Question

A movie studio is comparing the box office performances of several of their titles. In particular, the studio wants to investigate which of their 2 most popular genres, drama and comedy, performs better. The studio will do so with the sample data below.

	n	x (in millions)	θ (In millions)
Drama	50	180	50
Comedy	30	150	30

Does the sample data provide evidence that the studios drama titles earn more than 10 million dollars more per movie than their comedy titles? Test the relevant hypotheses using a= 0.05

Answer 1

Ho: mu1-mu2=0 #mean of drama and comedy movie are equal

H1: mu1-mu2 >=0mean of drama movie is larger than mean  of comedy movie

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 50 180.0 50.0 7.1
2 30 150.0 30.0 5.5

Difference = mu (1) - mu (2)
Estimate for difference: 30.0000
95% lower bound for difference: 15.1088
T-Test of difference = 0 (vs >): T-Value = 3.35 P-Value = 0.001 DF = 77

Conclusion: p-value< l.o.s=0.05, we reject Ho, hence we conclude that mean of drama movie is larger than mean of comedy movie.