Chapter 9: Q. 9. (page 564)

No homework? Refer to Exercise 1. The math teachers inspect the
homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework. A significance test yields a P-value of 0.1265.
a. Explain what it would mean for the null hypothesis to be true in this setting.
b. Interpret the P-value.

Short Answer

Expert verified

Part a) $H_{0} : p = 75 % = 0.75$

Part b)

Step by step solution

Part a) Step 1: Given information

The claim is proportion is less than $75 %$

Part a) Step 2: The objective is to explain the mean for the null hypothesis to be true in this setting.

The null hypothesis statement states that the population value is equal to the claim value:

$H_{0} : p = 75 % = 0.75$

If the null hypothesis $H_{0} : p = 75 % = 0.75$ is correct,

then $75 %$ of all students at the researcher's school finished their homework assignments last night.

part b) Step 1: Given information

$P - v a l u e = 0.1265 = 12.65 %$

$\hat{p} = 68 % = 0.68$

Part b) Step 2: The objective is to explain the p value

The claim is proportion is less than $75 %$

The null hypothesis or the alternative hypothesis is the claim. The null hypothesis statement states that the population is equal to the claim value. If the claim is the null hypothesis, then the alternative hypothesis statement is the inverse of the null hypothesis.

$H_{0} : p = 75 % = 0.75 H_{a} : p < 0.75$

When the null hypothesis is true, the P-value is the probability of receiving the value of the test statistic or a more extreme value.

When the population proportion of all students at the school who finished their homework assignments last night is $0.75$ , there is a $12.65 %$ chance that the sample proportion of students in the sample who finished their homework assignments last night is $0.68$ or less.