Q. 67 - The Practice of Statistics for AP

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.

Step-by-Step Solution

Answer

a. $z=2.41$

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

Step 1: 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 $29.8$.

Step 2: Explanation (part a)

Test statistic:

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

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

Step 3: 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:

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