test yourself! practice tool\nthe table below shows the results of a random sample of 160 teenagers.\n|…

test yourself! practice tool\nthe table below shows the results of a random sample of 160 teenagers.\n| |like to surf|do not like to surf|total|\n|--|--|--|--|\n|boys|80|25|105|\n|girls|45|10|55|\n|total|125|35|160|\nbased on the information given, which of the following statements are true? select all that apply.\n□ 66% of the participants were boys.\n□ 35% of the participants do not like to surf.\n□ $\frac{80}{105}$ of the boys like to surf.\n□ $\frac{10}{35}$ of the participants who do not like to surf were girls.\n□ the proportion of boys who like to surf is greater than the proportion of girls who like to surf.

test yourself! practice tool\nthe table below shows the results of a random sample of 160 teenagers.\n| |like to surf|do not like to surf|total|\n|--|--|--|--|\n|boys|80|25|105|\n|girls|45|10|55|\n|total|125|35|160|\nbased on the information given, which of the following statements are true? select all that apply.\n□ 66% of the participants were boys.\n□ 35% of the participants do not like to surf.\n□ $\frac{80}{105}$ of the boys like to surf.\n□ $\frac{10}{35}$ of the participants who do not like to surf were girls.\n□ the proportion of boys who like to surf is greater than the proportion of girls who like to surf.

Answer

Explanation:

Step1: Calculate percentage of boys

The total number of participants is 160, and the number of boys is 105. The percentage of boys is $\frac{105}{160}\times100%=\frac{10500}{160}% = 65.625%\neq66%$.

Step2: Calculate percentage of participants who don't like to surf

The number of participants who don't like to surf is 35. The percentage is $\frac{35}{160}\times 100%=\frac{3500}{160}%=21.875%\neq35%$.

Step3: Check proportion of boys who like to surf

The number of boys is 105 and the number of boys who like to surf is 80. The proportion of boys who like to surf is $\frac{80}{105}$.

Step4: Check proportion of girls among non - surfers

The number of participants who don't like to surf is 35, and the number of girls who don't like to surf is 10. The proportion of girls among non - surfers is $\frac{10}{35}$.

Step5: Compare proportions of boys and girls who like to surf

The proportion of boys who like to surf is $\frac{80}{105}\approx0.762$, and the proportion of girls who like to surf is $\frac{45}{55}\approx0.818$. So the proportion of boys who like to surf is less than the proportion of girls who like to surf.

Answer:

$\frac{80}{105}$ of the boys like to surf, $\frac{10}{35}$ of the participants who do not like to surf were girls.