Question

Attitudes In the study of older students’ attitudes from Exercise $63$, the sample mean SSHA score was $125.7$and the sample standard deviation was $29.8$.

(a) Calculate the test statistic.

(b) Find the P-value using Table $B$. Then obtain a more precise P-value from your calculator.

Short answer

a.$z=2.41$

b.$p-value=0.0101$. Using calculator$p-value=0.0080$

Step-by-step solution

Given information

Attitudes In the study of older students’ attitudes from Exercise $63$, the sample mean SSHA score was $125.7$and the sample standard deviation was $29.8$.

Explanation (part a)

Test statistic:

The $Z$score is shown below by plugging the known values:

$z=\frac{\overline{x}-{\mu }_o}{\sigma /\sqrt{n}}=\frac{125.7-115}{29.8/\sqrt{45}}=2.41$

Explanation (part b)

p-value approach:

$\begin{array}{r}p\text{-value}=P(z\ge 2.41)\\ =1-P(z\le 2.41)\\ =1-.9899=.0101\end{array}$

Use Table $B$to find the above p-value.

Reject$H_0$

Conclusion: $\mu >115$

To obtain a more precise p-value from your calculator:

$\begin{array}{r}p\text{-value}=P(z\ge 2.41)\\ =1-P(z\le 2.41)\\ =1-.9920=.0080\end{array}$