Question

Suppose that 20% of students at high school A and 18% of students at high school B participate on a school athletic team. Independent random samples of 30 students from each school are selected and asked if they participate on a school athletic team. Let ˆ p A represent the sample proportion of students at school A who participate on a school athletic team and ˆ p B represent the sample proportion of students at school B who participate on a school athletic team.

What is the value of n A p A ?

What is the value of n A ( 1 − p A ) ?

What is the value of n B p B ?

What is the value of n B ( 1 − p B ) ?

Is the shape of the sampling distribution approximately Normal?

____, these values _____ all at least 10.

Answer 1

6 ; 24 ; 5.4 ; 24.6

Explanation:

Given that:

Number of samples from each high school = 30

Proportion of students from high school A = 20%

Proportion of students from high school B = 18%

Number of sample A ; n(A) = 30

Proportion of sample A ; p(A) = 0.20

Number of sample B ; n(B) = 30

Proportion of sample B ; p(B) = 0.18

1.)

n(A).p(A) = 30 * 0.20 = 6

2.)

n(A). (1 - p(A))

30 * (1 - 0.20)

30 * 0.8 = 24

3.)

n(B).p(B) = 30 * 0.18 = 5.4

4.)

n(B). (1 - p(B))

30 * (1 - 0.18)

30 * 0.82

= 24.6

Shape of sampling distribution is not approximately normal ;

Both nApA and nBpB are < 10