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The Practice of Statistics for AP

Found in: Page 564

Book edition 4th

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

Pages 809 pages

ISBN 9781319113339

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Short Answer

After once again losing a football game to the archrival, a college’s alumni association conducted a survey to see if alumni were in favor of firing the
coach. An SRS of 100 alumni from the population of all living alumni was taken, and 64 of the alumni in the sample were in favor of firing the coach.
Suppose you wish to see if a majority of living alumni are in favor of firing the coach. The appropriate test statistic is
a. $z = \frac{0.64 - 0.5}{\sqrt{\frac{0.64 (0.36)}{100}}}$
b. $t = \frac{0.64 - 0.5}{\sqrt{\frac{0.64 (0.36)}{100}}}$
c. $z = \frac{0.64 - 0.5}{\sqrt{\frac{0.5 (0.5)}{100}}}$
d. $z = \frac{0.64 - 0.5}{\sqrt{\frac{0.64 (0.36)}{64}}}$
e. $z = \frac{0.5 - 0.64}{\sqrt{\frac{0.5 (0.5)}{100}}}$

Option a is correct

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Test statsitic

The test statistic for the population proportion is as follows:

$z = \frac{p - \hat{p}}{\sqrt{\frac{p (1 - p)}{100}}}$

where $p = 0.64$ , role="math" localid="1654256041572" $\hat{p} = 0.5$ and $n = 100$ .

Step 2. Substitute the value in the test statistic.

Substitute the respective values in the test statistic.

$\begin{matrix} z = \frac{0.64 - 0.5}{\sqrt{\frac{0.64 (1 - 0.64)}{100}}} \\ = \frac{0.64 - 0.5}{\sqrt{\frac{0.64 \times 0.36}{100}}} \end{matrix}$

So, option a is the correct option.

Most popular questions for Math Textbooks

Does Friday the $13 t h$ have an effect on people's behavior? Researchers collected data on the numbers of shoppers at a sample of $45$ different grocery stores on Friday the $6 t h$ and Friday the $13 t h$ in the same month. The dotplot and computer output below summarize the data on the difference in the number of shoppers at each store on these two days (subtracting in the order $6 t h$ minus $13 t h$ ).

Researchers would like to carry out a test of $H_{0} : μ_{d} = 0$ versus $H_{α} : μ_{d} \neq 0$ , where $μ_{d}$ is the true mean difference in the number of grocery shoppers on these two days. Which of the following conditions for performing a paired $t$ test is not met?

1. Random

II. Normal

III. Independent

(a) I only

(b) II only

(c) III only

d) I and II only

(e) I, II, and III

Eye black Athletes performing in bright sunlight often smear black grease under their eyes to reduce glare. Does cye black work? In one experiment, 16 randomly selected student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye black. Here are the differences in sensitivity, with eye black mines without eye black:

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.

- Interpret a Type l error and a Type ll error in context, and give the consequences of each.

- Understand the relationsonship between the significance level at a test P(Type li error), and power.

Is your food safe? Do you feel confident or not confident that the food available at most grocery stores is safe to eat? when a gallup poll asked this question, $87 %$ of the sample said they were confident." Callup announced the poll's margin of error for $95 %$ confidence as $\pm 3$ percentage points. Which of the following sources of error are included in this margin of error? Explain.

(a) Gallup dialed landline telephone numbers at random and so missed all people without landline phones, including people whose only phone is a cell phone.

(b) Some people whose numbers were chosen never answered the phone in several calls or answered but refused to participate in the poll.

(c) There is chance variation in the random selection of telephone numbers.

Which of the following $95 %$ confidence intervals would lead us to reject H0 : $p = 0.30$ in favor of

Ha :p not equal to $0.30$ at the $5 %$ significance level?

(a) (0.29, 0.38) (c) (0.27, 0.31) (e) N o n e o f t h e s e (b) (0.19, 0.27) (d) (0.24, 0.30)

Write a few sentences comparing what the P-values in Exercises 13 and 14 tell you about statistical significance in each of the two studies.

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