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Q. 10.

Expert-verifiedFound in: Page 564

Book edition
6th

Author(s)
Daren Starnes, Josh Tabor

Pages
837 pages

ISBN
9781319113339

Attitudes Refer to Exercise 4. In the study of older students’ attitudes, 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. Explain what it would mean for the null hypothesis to be true in this setting.

b. Interpret the P-value.

Part a) The correct mean score for the students who are at least $30$ years of age is $115$

Part b) The P-value is if the population mean is equal to$115$, then there is the possibility of$1.01\%$of getting a random sample with a sample mean of$125.7$ or more.

From the previous exercise,

${H}_{0}:\mu =115\phantom{\rule{0ex}{0ex}}{H}_{a}:\mu >115$

$\mu $ is the population mean score of students who are at least 30 years of age.

If the null hypothesis ${H}_{0}:\mu =115$is correct, the true mean score for students who are at least $30$years old is$115$

$n=45\phantom{\rule{0ex}{0ex}}\overline{x}=125.7\phantom{\rule{0ex}{0ex}}s=29.8\phantom{\rule{0ex}{0ex}}P=0.0101=1.01\%$

Result of the previous exercise:

${H}_{0}:\mu =115\phantom{\rule{0ex}{0ex}}{H}_{a}:\mu >115$

If the population means is$115$ then there is a $1.01\%$ chance of getting a random sample with a sample means of$125.7$ or higher.

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