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Q.10

Expert-verifiedFound in: Page 664

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.

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$

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:

$P>0.05\Rightarrow \text{Fail to reject}{H}_{0}$

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

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