Question

The two-way frequency table shows the results

of a random survey of movies watched by
100 students. Mrs. Leary said that according
to the data, girls are more likely than boys to
watch movie A. Is the statement true or false?
Explain.
A
Boys
14
Girls 16
Total 30
B
12
22
34
C
19
17
36
Total
45
55
100

Answer 1

Mrs. Leary's statement that girls are more likely than boys to watch movie A is false. The proportion of boys who watched movie A is higher than the proportion of girls, according to the frequency table provided.

Step-by-step explanation:

The student is asking whether Mrs. Leary's statement that girls are more likely than boys to watch movie A is true or false based on the data from a two-way frequency table. To assess this, one must compare the proportion of girls who watched movie A to the proportion of boys who did the same.

According to the table, 14 boys watched movie A out of a total of 45 boys. The proportion of boys who watched movie A is 14/45. For girls, 16 out of a total of 55 watched movie A, and the proportion of girls who watched movie A is 16/55.

Calculating these proportions:
Boys: 14/45 ≈ 0.3111
Girls: 16/55 ≈ 0.2909

Since 0.3111 (boys) > 0.2909 (girls), it can be concluded that a higher proportion of boys watched movie A compared to girls. Therefore, Mrs. Leary's statement is false. Girls are not more likely than boys to watch movie A based on the survey results.