Chapter 13, Problem 184CE

a:

To determine

Calculate the z value and p value with boys.

Explanation of Solution

The null hypothesis (H₀) is $\left({\text{p}}_1-{\text{p}}_2\right)=0$ and the alternate hypothesis (H₁)is $\left({\text{p}}_1-{\text{p}}_2\right)>0$.

The calculated Z value and p value can be obtained using the statistical software. The result is given below:

The Z value is 2.49 and the p value is 0.0065. Since the p value is nearly equal to 0, the alternate hypothesis is accepted.

b:

To determine

Calculate the z value and p value with girls.

Explanation of Solution

The null hypothesis (H₀) is $\left({\text{p}}_1-{\text{p}}_2\right)=0$ and the alternate hypothesis (H₁)is $\left({\text{p}}_1-{\text{p}}_2\right)>0$.

The calculated Z value and p value can be obtained using the statistical software. The result is given below:

The Z value is 0.893 and the p value is 0.1859. Since the p value is significantly different from 0, the alternate hypothesis is not accepted.

c:

To determine

Calculate the z value and p value with boys and girls.

Explanation of Solution

The null hypothesis (H₀) is $\left({\text{p}}_1-{\text{p}}_2\right)=0$ and the alternate hypothesis (H₁)is $\left({\text{p}}_1-{\text{p}}_2\right)>0$.

The calculated Z value and p value can be obtained using the statistical software. The result is given below:

The Z value is 2.61 and the p value is 0.0045. Since the p value is nearly equal to 0, the alternate hypothesis is accepted.