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Q.10

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The Practice of Statistics for AP

Found in: Page 664

Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

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Short Answer

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.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

Step 2: Explanation

The hypotheses:

$H_{0} : μ_{1} = μ_{2}$

$H_{1} : μ_{1} \neq μ_{2}$

The test statistic:

$t = \frac{{\bar{x}}_{1} - {\bar{x}}_{2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{1}}}}$

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

$= - 0.8276$

Step 3: Explanation

Degrees of freedom:

$d f = 62.8$

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:

$P > 0.05 \Rightarrow Fail to reject H_{0}$

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

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