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Q.1

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The Practice of Statistics for AP

Found in: Page 594

Book edition 4th

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

Pages 809 pages

ISBN 9781319113339

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Short Answer

Stating hypotheses State the appropriate null and alternative hypotheses in each of the following cases.
(a) The average height of $18$ -year-old American women is $64.2$ inches. You wonder whether the mean height of this year's female graduates from a large local high school (over $3000$ students) differs from the national average. You measure an SRS of $48$ female graduates and find that $X = 63.1$ inches.
(b) Mr. Starnes believes that less than $75 %$ of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of students at the school to help Mr. Starnes test his claim.
- Check conditions for carrying out a test about a population proportion or mean.
- Interpret $P$ -values in context.

(a) $H_{0} : μ = 64.2$

$H_{α} \neq 64.2$

(b) $H_{0} : P = 0.75$

$H_{α} : P < 0.75$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part (a)Step 1 :Given information

Given in the question that,

Population mean $(μ) = 64.2$

Sample mean $(x) = 63.1$

Sample size $(n) = 48$ we have to find an SRS of $48$ female graduates and find that $\bar{X} = 63.1$ inches.

Part (a) Step2 :Explanation

Consider $μ$ be the average height of $18$ year old american women. using the information, the null and alternative hypothesis are:

$H_{0} : μ = 64.2$

$H_{α} : μ \neq 64.2$

Part (b) Step 1:Given Information

Given in the question that, population proportion $= 0.75$

Part (b) Step 2:Explanation

Here, $p$ be the population proportion of the students that completed their homework last night.

Using the information, the null and alternative hypotheses are:

$H_{α} : P = 0.75$

$H_{α} : P < 0.75$

Most popular questions for Math Textbooks

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over $1000$ Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of one inch could be increased by

(a) using only volunteers from the basketball team in the experiment.

(b) using $A = 0.01$ instead of $A = 0.05$ .

(c) using $A = 0.05$ instead of $A = 0.01$ .

(d) giving the drug to $25$ randomly selected students instead of $50$ .

(e) using a two-sided test instead of a one-sided test.

Refer to Exercise 2. For Yvonne's survey, 96 students in the sample said they rarely or never argue with friends. A significance test yields a P-value of 0.0291.

(a) Interpret this result in context.

(b) Do the data provide convincing evidence against the null hypothesis? Explain.

Does this paper give convincing evidence that the mean amount of sugar in the hindguts under these conditions is not equal to $7 m g$ ? Justify your answer.

Attitudes The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students’ attitudes toward school and study habits. Scores range from $0 t o 200$ . The mean score for U.S. college students is about $115$ . A teacher suspects that

older students have better attitudes toward school. She gives the SSHA to an SRS of $45$ of the over $1000$ students at her college who are at least $30$ years of age. Check the conditions for carrying out a significance test of the teacher’s suspicion.

An SRS of 100 postal employees found that the average time these employees had worked at the postal service was $7$ years with standard deviation $2$ years. Do these data provide convincing evidence that the mean time of employment M for the population of postal employees has changed from the value of $7.5$ that was true $20$ years ago? To determine this, we test the hypotheses $H_{0} : μ = 7.5$ versus $H_{a} : μ \neq 7.5$ using a one-sample $t$ test. What conclusion should we draw at the $5 %$ significance level?

(a) There is convincing evidence that the mean time working with the postal service has changed.

(b) There is not convincing evidence that the mean time working with the postal service has changed.

(c) There is convincing evidence that the mean time working with the postal service is still $7.5$ years.

(d) There is convincing evidence that the mean time working with the postal service is now $7$ years.

(e) We cannot draw a conclusion at the $5 %$ significance level. The sample size is too small.

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