Select all the correct answers.
A radio station surveyed a group of men and women, asking them to name the genre of music they prefer. This table shows the survey results.
Pop Jazz Rock Hip-Hop
Men 16 38 101 45
Women 91 48 22 39
Which statements about this data are true? Round your answers to the nearest hundredth.
A. The relative frequency of people who prefer jazz who are women is 0.24.
B. The relative frequency of men who prefer hip-hop is 0.54.
C. The relative frequency of people who prefer rock who are men is 0.50.
D. The relative frequency of women who prefer pop is 0.46.
E. The relative frequency of people who prefer hip-hop who are women is 0.46.
A. False - the relative frequency of women who prefer jazz is 48/(91+48+22+39) = 0.30 (rounded to the nearest hundredth).
B. True - the relative frequency of men who prefer hip-hop is 45/(16+38+101+45) = 0.54 (rounded to the nearest hundredth).
C. True - the relative frequency of men who prefer rock is 101/(16+38+101+45) = 0.50 (rounded to the nearest hundredth).
D. True - the relative frequency of women who prefer pop is 91/(91+48+22+39) = 0.46 (rounded to the nearest hundredth).
E. False - the relative frequency of women who prefer hip-hop is 39/(91+48+22+39) = 0.16 (rounded to the nearest hundredth).
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To determine whether each statement is true or false, we need to calculate the relative frequencies for each preference within the given group (men or women) and compare the calculated values with the statement's given values.
1. To calculate the relative frequency, we divide the frequency (number of individuals) who prefer a particular genre by the total number of individuals in that group (men or women) and round to the nearest hundredth.
A. To calculate the relative frequency of people who prefer jazz and are women:
Relative frequency = (Number of women who prefer jazz) / (Total number of women)
= 48 / (91 + 48 + 22 + 39)
≈ 0.2424 (rounded to the nearest hundredth)
Comparing this value to the given 0.24, we can conclude that Statement A is true.
B. To calculate the relative frequency of men who prefer hip-hop:
Relative frequency = (Number of men who prefer hip-hop) / (Total number of men)
= 45 / (16 + 38 + 101 + 45)
≈ 0.2391 (rounded to the nearest hundredth)
Comparing this value to the given 0.54, we can conclude that Statement B is false.
C. To calculate the relative frequency of people who prefer rock and are men:
Relative frequency = (Number of men who prefer rock) / (Total number of men)
= 101 / (16 + 38 + 101 + 45)
≈ 0.4131 (rounded to the nearest hundredth)
Comparing this value to the given 0.50, we can conclude that Statement C is false.
D. To calculate the relative frequency of women who prefer pop:
Relative frequency = (Number of women who prefer pop) / (Total number of women)
= 91 / (91 + 48 + 22 + 39)
≈ 0.4727 (rounded to the nearest hundredth)
Comparing this value to the given 0.46, we can conclude that Statement D is false.
E. To calculate the relative frequency of people who prefer hip-hop and are women:
Relative frequency = (Number of women who prefer hip-hop) / (Total number of women)
= 39 / (91 + 48 + 22 + 39)
≈ 0.2021 (rounded to the nearest hundredth)
Comparing this value to the given 0.46, we can conclude that Statement E is false.
Therefore, the correct answers are:
A. The relative frequency of people who prefer jazz who are women is 0.24.
C. The relative frequency of people who prefer rock who are men is 0.50.
D. The relative frequency of women who prefer pop is 0.46.