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.

Short 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$\alpha =0.01$

Step-by-step solution

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 = role="math" localid="1654319413192" $0.0101=1.01\%$

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$\alpha =0.01$