Question

KY Freshman girls and boys were surveyed to choose their favorite subjects from the list of Math, English or Science. Math English Science Total Girls 60 150 Boys 65 30 Totals 115 315 1. **Finish filling in the chart below. 2. What percent of the freshman class prefer English? Identify if this value represents a joint, marginal, or conditional relative frequency. 65 3. In the context of the data, interpret the conditional relative frequency of 115

Answer 1

1) First, we finish filling in the chart as shown below

| Math | English | Science | Total

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| Girls |115-65=50 | 150-(60+50)=40 | 60 | 150 |

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| Boys | 65 | 30 | 165-(65+30) = 70 | 315-150= 165 |

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| Totals | 115 | 40+30=70 | 60+70=130 | 315 |

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2) the total number of freshmen that prefer English = 70

the size of the freshman class = 315

Therefore,

`\text{ the percent of the freshman class that prefer English = }(70)/(315)*100\text{ \%}=22.22\text{ \%}`

In a two-way frequency table, the values in the totals row and column are marginal except for the total of everything at the lower right corner.

Hence, the percent of the freshman class that prefer English is 22.22 % and it represents a marginal frequency

3) This conditional relative frequency is the percent of freshmen who enjoy Math that are boys

4) the number of freshmen who enjoy science = 130

the number of freshmen who enjoy science that are boys = 70

Therefore,

`=\text{ the percent of freshmen who enjoy science that are boys }=(70)/(130)*100\text{ \%}=53,65\text{ \%}`

the percent of freshmen who enjoy science that are boys = 53.85 %

5) The number of students that like Math = 115

the total number of students = 315

`\text{ the probability }=(115)/(315)=0.3651`

Hence, the likelihood that the student's response will be math is 0.3651