Question

a movie - producer conducted a survey after the screening of his movie to find out how the film would be received by viewers from different age groups. the columns in the two - way table indicate the numbers of viewers who rated the film on a four - point scale: excellent, good, average, and poor.

viewers age group	excellent	good	average	poor	marginal totals
26 - 35	33	50	5	9	97
36 - 45	58	12	28	34	132
46 - 55	25	17	22	12	76
56 and above	12	5	3	8	28
marginal totals	160	126	70	70	446

2
select the correct answer
which of these observations is supported by the data in the table?
note: a rating of good or excellent means the audience liked the movie, while a rating of poor means the audience disliked the movie.
a. among those who liked the movie, the majority were in the oldest age group.
b. among those who disliked the movie, the majority were in the 26 - 35 age group.
c. the majority of the audience in the 16 - 25 age group liked the movie.
d. the majority of the audience in the 26 - 35 age group disliked the movie.

Explanation:

Step1: Calculate number who liked movie in each age - group

For 16 - 25 age group: $52 + 42=94$.
For 26 - 35 age group: $33 + 50 = 83$.
For 36 - 45 age group: $58+12 = 70$.
For 46 - 55 age group: $25 + 17=42$.
For 56 and above age group: $12 + 5 = 17$.

Step2: Analyze Option A

Among those who liked the movie, the 16 - 25 age group has the highest number ($94$), not the oldest age - group. So, Option A is incorrect.

Step3: Calculate number who disliked movie in each age - group

For 16 - 25 age group: $7$.
For 26 - 35 age group: $9$.
For 36 - 45 age group: $34$.
For 46 - 55 age group: $12$.
For 56 and above age group: $8$.
Among those who disliked the movie, the 36 - 45 age group has the highest number ($34$), not the 26 - 35 age group. So, Option B is incorrect.

Step4: Analyze Option C

In the 16 - 25 age group, the number of people who liked the movie ($52 + 42=94$) is greater than the number of people who disliked it ($7$). So, the majority of the audience in the 16 - 25 age group liked the movie. Option C is correct.

Step5: Analyze Option D

In the 26 - 35 age group, the number of people who liked the movie ($33 + 50 = 83$) is greater than the number of people who disliked it ($9$). So, the majority of the audience in the 26 - 35 age group liked the movie, not disliked it. Option D is incorrect.

Answer:

C. The majority of the audience in the 16 - 25 age group liked the movie