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Q 104.

Expert-verified

The Practice of Statistics for AP Examination

Found in: Page 610

Book edition 6th

Author(s) Daren Starnes, Josh Tabor

Pages 837 pages

ISBN 9781319113339

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Short Answer

You are testing $H_{0} : μ = 10$ against $H_{a} : μ \neq 10$ based on an SRS of $15$
observations from a Normal population. What values of the t statistic are statistically significant at the $α = 0.005$ level?
$a . t > 3.326 b . t > 3.286 c . t > 2.977 d . t < - 3.326 o r t > 3.326 e . t < - 3.286 o r t > 3.286$

The correct option is (d) $t < - 3.326 o r t > 3.326$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

Sample size $(n) = 15$

Level of significance $(α) = 0.05$

The null and alternative hypotheses are:

H_{0} : μ = 10 H_{a} : μ \neq 10

Step 2: Explanation

The degree of freedom is:

$D e g r e e o f f r e e d o m (d f) = n - 1 = 15 - 1 = 14$

The critical value at a $5 %$ significance level and $14$ degrees of freedom can be calculated using the critical value table as follows:

$t_{α / 2}, d f = t_{0.05 / 2}, 14 = \pm 3.326$

The test would be significant for the values $t < - 3.286$ or $t > 3.326$

Hence, the correct option is (d).

Most popular questions for Math Textbooks

Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults.

a. State appropriate hypotheses for testing the company’s claim. Be sure to define your parameter.

b. Describe a Type I error and a Type II error in this setting, and give the consequences Page Number: 615 of each.

c. Would you recommend a significance level of 0.01, 0.05, or 0.10 for this test? Justify your choice.

d. The power of the test to detect the fact that only 3% of adults who use this vaccine would develop flu using α=0.05 is 0.9437. Interpret this value.

e. Explain two ways that you could increase the power of the test from part (d).

Significance tests A test of $H_{o} : p = 0.5$ versus $H_{a} : p > 0.5$ based on

a sample of size $200$ yields the standardized test statistic $z = 2.19$ . Assume that the conditions for performing inference are met.

a. Find and interpret the P-value.

b. What conclusion would you make at the $α = 0.01$ significance level? Would

your conclusion change if you used α=0.05 instead? Explain your reasoning.

c. Determine the value of p^= the sample proportion of successes.

The standardized test statistic for a test of $H_{0} : p = 0.4$ versus $H_{a} : p n o t e q u a l t o 0.4$ is $z = 2.43$ This test is

a. not significant at either $α = 0.05$ or $α = 0.01$

b. significant at $α = 0.05$ but not at $α = 0.01$

c. significant at $α = 0.01$ but not at $α = 0.05$

d. significant at both $α = 0.05$ and $α = 0.01$

e. inconclusive because we don’t know the value of $\hat{p}$

Better parking A local high school makes a change that should improve student

satisfaction with the parking situation. Before the change, $37 %$ of the school’s students approved of the parking that was provided. After the change, the principal surveys an SRS of $200$ from the more than $2500$ students at the school. In all, $83$ students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective.

a. Describe a Type I error and a Type II error in this setting, and give a possible

consequence of each.

b. Is there convincing evidence that the principal’s claim is true?

Walking to school A recent report claimed that $13 %$ of students typically walk to school. DeAnna thinks that the proportion is higher than $0.13$ at her large elementary school. She surveys a random sample of $100$ students and finds that $17$ typically walk to school. DeAnna would like to carry out a test at the $α = 0.05$ significance level of $H_{0} : p = 0.13$ versus $H_{a} : p > 0.13$ , where $p$ = the true proportion of all students at her elementary school who typically walk to school. Check if the conditions for performing the significance test are met.

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