Q.13 - The Practice of Statistics for AP

Question

Attitudes In the study of older students’ attitudes from Exercise 3, 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) Interpret the P-value in context.

(b) What conclusion would you make if $\alpha$=0.05? If data-custom-editor="chemistry" $\mathrm{\alpha }$=0.01? Justify your answer.

Step-by-Step Solution

Answer

a. When the population mean is$115$, there is a $1.01\%$chance of getting a sample mean of $125.7$

b. Enough convincing evidence against the null hypothesis when $\alpha =0.05$ and not enough convincing evidence against the null hypothesis when $\alpha =0.01$

Part (a) Step 1: Given Information

Sample mean = $125.7$

Sample standard deviation = $29.8$

P-value = $0.0101$

Part (a) Step 2: Explanation

The sample mean $\stackrel{-}{x}$= $125.7$

standard deviation $\sigma =29.8$

P-value = $0.0101=1.01\%$

Calculating the null and alternative hypotheses,

$\begin{array}{rl}& H_o:\mu =115\\ & H_a:\mu >115\end{array}$

Hence when the population mean is$115$, there is a $1.01\%$ chance of getting a sample mean of $125.7$

Part (b) Step 1: Given Information

Sample mean = $125.7$

Sample standard deviation = $29.8$

P-value = $0.0101=1.01\%$

Part (b) Step 2: Explanation

The p-value = $0.0101$

When $\alpha =0.05$

The p-value is less than $\alpha =0.005$

The null hypothesis is rejected

When $\alpha =0.01$$\alpha =0.01$

The p-value is greater than $\alpha =0.01$

The null hypothesis is not rejected

Hence there is enough convincing evidence against the null hypothesis when $\alpha =0.05$ and not enough convincing evidence against the null hypothesis when $\alpha =0.01$