Question

the majoring in money study by sallie mae from december 2015 showed that most college students manage their credit cards in a reasonable way. it showed 23% of students who own credit cards make partial payments that exceed the maximum amount due. you are curious to find out if the proportion of students who make partial payments that exceed the minimum amount has decreased since 2015 and collect data from a random sample of 380 students. you find that 70 students are making partial payments on their credit cards that exceed the minimum amount due. using $\alpha = 0.01$, complete parts a and b below. calculate the test statistic. $z_0=-2.12$ (type an integer or decimal rounded to two decimal places as needed.) determine the conclusion. choose the correct answer below. a. reject $h_0$. there is sufficient evidence to conclude that the proportion of students who make partial payments that exceed the minimum amount has decreased since 2015. b. do not reject $h_0$. there is not sufficient evidence to conclude that the proportion of students who make partial payments that exceed the minimum amount has decreased since 2015. c. do not reject $h_0$. there is sufficient evidence to conclude that the proportion of students who make partial payments that exceed the minimum amount has decreased since 2015. d. reject $h_0$. there is not sufficient evidence to conclude that the proportion of students who make partial payments that exceed the minimum amount has decreased since 2015.

Explanation:

Step1: Find the critical value

For a one - tailed test with $\alpha = 0.01$, the critical value $z_{\alpha}$ is $z_{0.01}=- 2.33$ (since it is a left - tailed test as we are checking if the proportion has decreased).

Step2: Compare the test statistic with the critical value

We are given the test statistic $z_{0}=-2.12$.
Since $z_{0}=-2.12>-2.33$ (i.e., the test statistic is not in the rejection region).

Answer:

B. Do not reject $H_{0}$. There is not sufficient evidence to conclude that the proportion of students who make partial payments that exceed the minimum amount has decreased since 2015.