Question

In the study of older students’ attitudes, the sample mean SSHA score was $125.7$and the sample standard deviation was $29.8$. A significance test yields a P-value of $0.0101$.

a. Explain what it would mean for the null hypothesis to be true in this setting.

b. Interpret the P-value.

Short answer

Part a. The correct mean score for the students who are at least $30$years of age is $115$.

Part b. The P-value is if the population mean is equal to$115$, then there is possibility of $1.01\%$of getting a random sample with a sample mean of $125.7$or more.

Step-by-step solution

Part a. Step 1. Given information

From the previous exercise

$$\begin{gathered} H_0:\mu =115 \\ {H}_a:\mu >115 \end{gathered}$$

Part a. Step 2. Explanation

$\mu$is the population mean score of students who are at least $30$years of age.

If the null hypothesis $H_0:\mu =115$is true, then this means that the true mean score for students who are at least $30$years of age is$115$.

Part b. Step 1. Given information

$$\begin{gathered} n=45 \\ \overline{x}=125.7 \\ s=29.8 \\ P=0.0101=1.01\% \end{gathered}$$

Result previous exercise:

$$\begin{gathered} H_0:\mu =115 \\ {H}_a:\mu >115 \end{gathered}$$

Part b. Step 2. Explanation

The P-value is if the population mean is equal to $115$, then there is possibility of $1.01\%$of getting a random sample with a sample mean of$125.7$ or more.