Solution Found!

Statistics / Fundamentals of Statistics 4 / Chapter 10.2 / Problem 36AYU

Fundamentals of Statistics | 4th Edition | ISBN: 9780321838704 | Authors: Michael Sullivan,III

Change Question

Accept versus Do Not Reject In the United States,

Chapter , Problem 36AYU

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

Problem 36AYU

Problem

Accept versus Do Not Reject In the United States, historically, 40% of registered voters are Republican. Suppose you obtain a simple random sample of 320 registered voters and find 142 registered Republicans.

(a) Consider the hypotheses H0: p = 0.4 versus H1 p > 0.4. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of significance. Write a conclusion for the test.

(b) Consider the hypotheses H0: p = 0.41 versus H1 p > 0.41. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of significance. Write a conclusion for the test.

(c) Consider the hypotheses H0: p = 0.42 versus H1 p > 0.42. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of significance. Write a conclusion for the test.

(d) Based on the results of parts (a)-(c), write a few sentences that explain the difference between “accepting” the statement in the null hypothesis versus “not rejecting” the statement in the null hypothesis.

Questions & Answers

QUESTION:

Problem 36AYU

Problem

Accept versus Do Not Reject In the United States, historically, 40% of registered voters are Republican. Suppose you obtain a simple random sample of 320 registered voters and find 142 registered Republicans.

(a) Consider the hypotheses H0: p = 0.4 versus H1 p > 0.4. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of significance. Write a conclusion for the test.

(b) Consider the hypotheses H0: p = 0.41 versus H1 p > 0.41. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of significance. Write a conclusion for the test.

(c) Consider the hypotheses H0: p = 0.42 versus H1 p > 0.42. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of significance. Write a conclusion for the test.

(d) Based on the results of parts (a)-(c), write a few sentences that explain the difference between “accepting” the statement in the null hypothesis versus “not rejecting” the statement in the null hypothesis.

ANSWER:

Answer :

Step 1 :

Given, In the United States, historically, 40% of registered voters are Republican. Suppose you obtain a simple random sample of 320 registered voters and find 142 registered Republicans.

${p}_{0}$ = 40% = 0.4 and 1 - ${p}_{0}$ = 0.6

n = 320, x = 142 and $\alpha{}$ = 0.05

$n{p}_{0}(1-{p}_{0})\ >10$

$(320)(0.4)(1-0.4)\ >10$

76.8 > 10

The hypothesis be

${H}_{0}$ : p = 0.4

${H}_{1}$ : p > 0.4

n = 320, x = 142 and $\alpha{}$ = 0.05

Z = $\frac{(P\ -\ {P}_{0})}{\sqrt{\frac{{P}_{0}(1\ -\ {P}_{0})}{n}}}$

Where,

p = x/n = 142/320 = 0.4437 , ${P}_{0}$ = 0.4 and 1 - ${P}_{0}$ =0.6

then , Z = $\frac{(P\ -\ {P}_{0})}{\sqrt{\frac{{P}_{0}(1\ -\ {P}_{0})}{n}}}$

Z = $\frac{(0.4437\ -\ 0.4)}{\sqrt{\frac{0.4(0.6)}{320}}}$

= $\frac{0.0437}{0.02738}$ = 1.59

Calculated value is less than the table value

we reject the null hypothesis.

the p value for right tailed test is

Study Tools You Might Need

Chapter: 3 Problem: 38

College Physics 1
A football quarterback is moving straight backward at a speed of 2.00 m/s when he throws a pass to a player 18.0 m straight downfield. (a) If the ball is thrown at an angle of 25 relative to the ground and is caught at the same height as it is released, what is its initial speed relative to the groun

Chapter: 6 Problem: 6.41

Mathematical Statistics with Applications 7
Let \(Y_{1}, Y_{2^{\prime} \ldots}, Y_{n}\) be independent, normal random variables, each with mean \(\mu\) and variance \(\sigma^{2}\). Let \(a_{1}, a_{2}, \ldots, a_{n}\) denote known constants. Find the density function of the linear combination \(U=\sum_{i=1}^{n} a_{i} Y_{i}\). Equation Trans

Chapter: 5 Problem: 26P

Physics with MasteringPhysics 4
Problem 26P A surfer "hangs ten," and accelerates down the sloping face of a wave. If the surfer's acceleration is 3.25 m/s2 and friction can be ignored, what is the angle at which the face of the wave is inclined above the horizontal?

Chapter: 11 Problem: 7

Physics: Principles with Applications 7
A mass m at the end of a spring oscillates with a frequency of 0.83 Hz. When an additional 780-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?

Chapter: 29 Problem: 7

Principles of Economics 6
Bank A has a leverage ratio of 10, while Bank B has a leverage ratio of 20. Similar losses on bank loans at the two banks cause the value of their assets to fall by 7 percent. Which bank shows a larger change in bank capital? Does either bank remain solvent? Explain.

Chapter: 8 Problem: 79

The Practice of Statistics 5
Watching TV (6.1, 7.3) Choose a young person (aged 19 to 25) at random and ask, In the past seven days, how many days did you watch television? Call the response X for short. Here is the probability distribution for X: 31 Days: 0 1 2 3 4 5 6 7 Probability: 0.04 0.03 0.06 0.08 0.09 0.08 0.05 ??? (a) W

Chapter: 13 Problem: 5

Psychology 5
Which of the following is a situational factor that influences attraction? a. proximity b. similarity c. bilateral symmetry d. personality

Chapter: 6 Problem: 6.28

Chemistry for today : general, organic, and biochemistry 9
A 2.50-L sample of neon at \(0.00^{\circ} \mathrm{C}\) and 1.00 atm is compressed into a 0.75-L cylinder. What pressure will the gas exert in the cylinder at \(30 .{ }^{\circ} \mathrm{C}\)?

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account