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. Viewer's Age Group Excellent Good Average Poor Marginal Totals 16-25 52 42 12 7 113 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 180 126 70 70 446 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.

Answer 1

The number of viewers from the 46 - 55 age group who rated the film excellent is 25.
Therefore, the percentage of the total survey group who rated the film excellent and also was from the 46-55 age group = 25 / 446 x 100% = 5.61%

Answer 2

Solution:

Viewer's Age Group Excellent Good   Average   Poor      Total

 16-25:                              52           42           12          7                113            

  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                180           126           70     70     446

% of people who liked the movie (rating of good or excellent)=$\frac{180+126}{446}\times100=\frac{306}{446}\times 100=68.60$

% of people who Disliked the movie (rating of Poor)=$\frac{70+70}{446}\times100=\frac{140}{446}\times 100=31.40$%

% of people in the age group(16-25) liked the movie (rating of good or excellent)=$\frac{52+42}{113}\times100=\frac{94}{113}\times 100=83.18$%

% of people age group(16-25) who Disliked the movie (rating of Poor)=100-83.18=16.82%

% of people in the age group(26-35) liked the movie (rating of good or excellent)=$\frac{50+33}{97}\times100=\frac{83}{97}\times 100=85.56$%

% of people age group(26-35) who Disliked the movie (rating of Poor)=100-85.56=14.44%

% of people in the age group(36-45) liked the movie (rating of good or excellent)=$\frac{58+12}{132}\times100=\frac{70}{132}\times 100=53.03$%

% of people age group(36-45) who Disliked the movie (rating of Poor)=100-53.03=46.97%

% of people in the age group(46-55) liked the movie (rating of good or excellent)=$\frac{25+17}{76}\times100=\frac{42}{76}\times 100=55.26$%

% of people age group(46-55) who Disliked the movie (rating of Poor)=100-55.26=44.74%

% of people in the age group(55 and above) liked the movie (rating of good or excellent)=$\frac{12+5}{28}\times100=\frac{17}{28}\times 100=60.71$%

% of people age group(55 and above) who Disliked the movie (rating of Poor)=100- 60.71=39.29%