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Q 105.

Expert-verified

The Practice of Statistics for AP Examination

Found in: Page 611

Book edition 6th

Author(s) Daren Starnes, Josh Tabor

Pages 837 pages

ISBN 9781319113339

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Short Answer

After checking that conditions are met, you perform a significance test of $H_{0} : μ = 1$ versus $H_{a} : μ \neq 1$ You obtain a $P -$ value of $0.022$ Which of the following must be true?
a. A $95 %$ confidence interval for $μ^{μ}$ will include the value $1$
b. A $95 %$ confidence interval for $μ^{μ}$ will include the value $0.022$
c. A $99 %$ confidence interval for $μ^{μ}$ will include the value $1$
d. A $99 %$ confidence interval for $μ^{μ}$ will include the value $0.022$
e. None of these is necessarily true.

The correct option is (c) A $99 %$ confidence interval for $μ^{μ}$ will include the value $1$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

$H_{0} : μ = 1 H_{a} : μ \neq 1 P = 0.022$

Step 2: Calculation

The null hypothesis is rejected if the $P -$ value is less than the significance level.

$P < 0.05 = 5 % r e j e c t H_{0} P > 0.01 = 1 % = f a i l s t o r e j e c t H_{0}$

A significance test at the $5 %$ significance level equates to a $95$ percent confidence interval.

A significance test at the $1 %$ significance level equates to a $99$ percent confidence interval.

There is no one in $95 %$ of the confidence interval.

There are $1$ in the $95 %$ confidence interval.

So correct option is (c).

Most popular questions for Math Textbooks

Heavy bread? The mean weight of loaves of bread produced at the bakery where you work is supposed to be $1$ pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees are producing loaves that are too light. Suppose you weigh an SRS of bread loaves and find that the mean weight is $0.975$ pound.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

b. Explain why there is some evidence for the alternative hypothesis.

c. The P-value for the test in part (a) is $0.0806$ . Interpret the P-value.

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

Which of the following has the greatest probability?

a. $P (t > 2)$ if t has 5 degrees of freedom.

b. $P (t > 2)$ if t has 2 degrees of freedom.

c. $P (z > 2)$ if z is a standard Normal random variable.

d. $P (t < 2)$ if t has 5 degrees of freedom.

e. $P (z < 2)$ if z is a standard Normal random variable.

Restaurant power Refer to Exercise $86$ Determine if each of the following changes would increase or decrease the power of the test. Explain your answers.

a. Use a random sample of $30$ people instead of $50$ people.

b. Try to detect that $μ = $ 85, 500$ instead of $μ = $ 86, 000$

c. Change the significance level to $α = 0.10$

Walking to school Refer to Exercise 36.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and $P$ -value.

c. What conclusion would you make?

Jump around Refer to Exercise 78.

a. Construct and interpret a $90 %$ confidence interval for the true mean vertical jump $μ$ (in inches) of the students at Haley, Jeff, and Nathan’s school. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) is consistent with the result of the test in Exercise $78$

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