Question

Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for

a. independent group means, population standard deviations, and/or variances known

b. independent group means, population standard deviations, and/or variances unknown

c. matched or paired samples

d. single mean

e. two proportions

f. single proportion

A high school principal claims that 30% of student athletes drive themselves to school, while 4% of non-athletes drive themselves to school. In a sample of 20 student athletes, 45% drive themselves to school. In a sample of 35 non-athlete students, 6% drive themselves to school. Is the percent of student athletes who drive themselves to school more than the percent of nonathletes?

Short answer

This is a Two proportions.

Step-by-step solution

Given information

According to a high school administrator, 30% of student athletes drive themselves to school, whereas only 4% of non-athletes drive themselves. 45 percent of a group of 20 student athletes drive themselves to school.

Indicate whether the hypothesis test was successful.

Let $p_a$ be the percentage of athletes who drive themselves to school.

Let$p_{na}$be the percentage of nonathletes who drive themselves to school.

The null and alternative hypothesis are then provided by,

$$\begin{gathered} H_o:p_a=p_{na} \\ {H}_1:p_a>p_{na} \end{gathered}$$

Hence the hypotheses test is for two proportions.