Question

A random sample of 300 students participated in a taste test. Each teenager sampled three different kinds of fruit smoothie and then were ask to pick a favorite. The table at left shows the results of the taste test. Based on the information given, which of the given statement is not true? A. About 67% of participants were girlsB. 20% of the participants preferred orange oasis C.3/4 of the boys preferred fruit fantasia D. 1/16 of the participants who preferred berry blast were boys

Answer 1

In order to prove which of the statements is not true, we need to prove each independently.

A. About 67% of the participants were girls.

In order to prove this, we need to divide the number of girls by the random sample and multiply by 100

`(200)/(300)\cdot100=66.67\approx67`

The statement is true.

B. 20% of the participants preferred orange oasis

To prove this statement, we should divide the total of orange oasis by the random sample as it refers to the participants and not a specific group, and then multiply by 100.

`(45)/(300)\cdot100=15`

The statement is false because 15% of the participants preferred orange oasis, not 20%.

C. 3/4 of the boys preferred fruit fantasy.

To prove this, we use the row of the boys and divide the number of boys that preferred fruit fantasy by the total number of boys inside the sample.

`(75)/(100)=0.75=(3)/(4)`

The statement is true.

D. 1/16 of the participants who preferred berry blast were boys

To prove this, we use the column of berry blast and divide the number of boys who preferred berry blast by the total of people inside the sample that preferred berry blast

`(10)/(160)=(1)/(16)`

the statement is true.

The correct answer is B.