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Q.1

Expert-verified

The Practice of Statistics for AP

Found in: Page 597

Book edition 4th

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

Pages 809 pages

ISBN 9781319113339

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Short Answer

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are
a). $H_{0} : \hat{p} = 0.5; H_{a} : \hat{p} > 0.5$
(b) $H_{0} : p = 0.5; H_{a} : p > 0.5$
(c) $H_{0} : p = 0.5; H_{a} : p < 0.5$
(d) $H_{0} : p = 0.5; H_{a} : p \neq 0.5$
(e) $H_{0} : p > 0.5; H_{a} : p = 0.5$

The null and alternative hypotheses you would use to test this claim are (b) $H_{0} : p = 0.5; H_{a} : p > 0.5$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

The hypotheses are statements about the population parameter:

$p$ : population proportion.

$μ :$ population mean.

$σ :$ population standard deviation.

Step 2: Explanation

The null hypothesis states that the population parameter is equal to the value mentioned in the claim:

H_{0} : p = 50 % = 0.50

The alternative hypothesis states the opposite of the null hypothesis (according to the claim):

H_{a} : p > 0.50

Therefore, the correct answer is (B).

Most popular questions for Math Textbooks

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0.07	0.64	-0.12	-0.05	-0.18	0.14	-0.16	0.03
0.05	0.02	0.43	0.24	-0.11	0.28	0.05	0.29

We want to know whether cye black increases sensitivity an the average.

(a) State hypotheses, Be sure to define the parameter.

(b) Check conditions for carrying out a significance test.

(c) The $P v a l u e$ of the test is $0.047$ . Interpet this value in context.

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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.

Normal body temperature (8.3) Check that the conditions are met for performing inference about the mean body temperature in the population of interest.

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.

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23.2	21.2	28.9	27.7	29.1	27.3	16.1	22.6	25.6	34.2	23.9	26.8
20.5	34.3	21.4	32.6	26.2	34.1	31.5	24.6	23.0	28.6	24.4	28.1

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