Question

4. To study whether movie ratings and release season influence the box office earnings, you gather data on 70 recent movies. You characterize each movie’s rating (G, PG, PG-13, R, or NC-17) and release season (summer or not summer).
   1. Complete the ANOVA table below by filling in the shaded boxes
   2. Find the appropriate critical value(s) [?=0.05]
   3. Does box office revenue significantly vary with rating, release season, or their interaction? Clearly answer for each

   4. 	SS	df	MS	F
      Rating	455
      Season	192.5
      Interaction	140

Answer 1

Required Formulae:

DF_rating = number of ratings - 1

DF_season = number of season - 1

DF_interaction = DF_rating * DF_season

	SS	df	MS	F	F-critical
Rating	455	5 - 1 = 4
Season	192.5	2 - 1 = 1
Interaction	140	4 * 1 = 4
Error	1050	69 - 4 - 1 - 4 = 60
Total	1837.5	70 - 1 = 69

a) ANOVA table:

	SS	df	MS	F
Rating	455	4	113.75	6.5
Season	192.5	1	192.5	11
Interaction	140	4	35	2
Error	1050	60	17.5
Interaction	1837.5	69

b) critical value:

Critical value for rating is 2.525.

Critical value for Season is 4.001

Critical value for interaction is 2.525

c)

i) Rating:

6.5 > 2.525

Therefore, we reject null hypothesis.

There is sufficient evidence to conclude that box office revenue vary with ratings of the movie.

ii) Season:

11 > 4.001

Therefore, we reject null hypothesis.

There is sufficient evidence to conclude that box office revenue vary with season in which movie releases.

iii) Interaction:

2 < 2.525

Therefore, we fail to reject null hypothesis.

There is sufficient evidence to conclude that box office revenue does not vary with interaction of season and movie rating.