Question

Attitudes Refer to Exercise 4. 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 the 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,

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

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

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

If the null hypothesis $H_0:\mu =115$is correct, the true mean score for students who are at least $30$years old is$115$

Part b) Step 1: Given information

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

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

Result of the previous exercise:

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

If the population means is$115$then there is a $1.01\%$chance of getting a random sample with a sample means of$125.7$ or higher.