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Q. 10.

Expert-verified
Found in: Page 564

### The Practice of Statistics for AP Examination

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.

See the step by step solution

## Part a) Step 1: Given information

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.

## Part a) Step 2: The objective is to explain the mean for the null hypothesis to be true in this setting

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

## Part b) Step 1: Given information

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

## Part b) Step 2: The objective is to explain the p value

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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