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Q.10

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Found in: Page 664

### The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339

# Students’ self-concept Here is SAS output for a study of the self-concept of a random sample of seventh-grade students. The variable SC is the score on the Piers-Harris Self-Concept Scale. The analysis was done to see if male and female students differ in mean self-concept score .Write a few sentences summarizing the comparison of females and males, as if you were preparing a report for publication

There is not enough proof to reject the claim that the population mean is equal for men and women.

See the step by step solution

## Step 2: Explanation

The hypotheses:

${H}_{0}:{\mu }_{1}={\mu }_{2}$

${H}_{1}:{\mu }_{1}\ne {\mu }_{2}$

The test statistic:

$t=\frac{{\overline{x}}_{1}-{\overline{x}}_{2}}{\sqrt{\frac{{s}_{1}^{2}}{{n}_{1}}+\frac{{s}_{2}^{2}}{{n}_{1}}}}$

$=\frac{55.516-57.915}{\sqrt{\frac{12.6962}{31}}+\frac{12.{265}^{2}}{47}}$

$=-0.8276$

## Step 3: Explanation

Degrees of freedom:

$df=62.8$

The P-value is the chance of having the test statistic's value, or a number that is more extreme.

$P=0.4110$

If the P-value is equal or les than to the significance level, then the null hypothesis is rejected:

$P>0.05⇒\text{Fail to reject}{H}_{0}$

There is not enough proof to reject the claim that the population mean is equal for men and women.