The Pew Research Center has reported results of many studies highlighting political topics and potential public policy. For example, when Gallup first surveyed public opinion about the legalization of marijuana in 1969, only 12% of the public favored legalization. A more recent survey from March 2016 showed 53% of the public favoring legalization of marijuana.To examine potential generational differences in the proportions who favor the legalization of marijuana, researchers randomly surveyed groups of Baby Boomers (those born between 1946 and 1964) and Millennials (those born from 1981 to 1997) asking the following question: "Do you support the legalization of marijuana for medical and recreational use in the United States?"The data were as follows. YesNoTotalBaby Boomers (population 1)312293605Millennials (population 2)349286635 (a)State the appropriate null and alternative hypotheses.H0: p1 ? < = > ≠p2Ha: p1 ? < = > ≠p2(b)Find the value of p̂1 and p̂2. (Enter your answers as fractions.)p̂1=p̂2=(c)Calculate the test statistic. (Round your answer to two decimal places.) (d)Based on ? = 0.05, what is the appropriate conclusion for the hypothesis test? (Use a table or SALT.)Accept the null hypothesis.Reject the null hypothesis. Fail to reject the null hypothesis.Fail to accept the null hypothesis. The Pew Research Center has reported results of many studies highlighting political topics and potential public policy. For example, when Gallup first surveyed public opinion about the legalization of marijuana in 1969, only 12% of thepublic favored legalization. A more recent survey from March 2016 showed 53% of the public favoring legalization of marijuana.To examine potential generational differences in the proportions who favor the legalization of marijuana, researchers randomly surveyed groups of Baby Boomers (those born between 1946 and 1964) and Millennials (those born from1981 to 1997) asking the following question: "Do you support the legalization of marijuana for medical and recreational use in the United States?"The data were as follows.YesNoTotalBaby Boomers (population 1)312293605Millennials (population 2)349286635In USE SALT(a) State the appropriate null and alternative hypotheses.Ho: P, ? vP2? VP2(b) Find the value of p, and p,. (Enter your answers as fractions.)1P 1P2%D(c) Calculate the test statistic. (Round your answer to two decimal places.)(d) Based on a = 0.05, what is the appropriate conclusion for the hypothesis test? (Use a table or SALT.)Accept the null hypothesis.Reject the null hypothesis.Fail to reject the null hypothesis.O Fail to accept the null hypothesis.O O

Name: The Pew Research Center has reported results of many studies highlight
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: The Pew Research Center has reported results of many studies highlighting political topics and potential public policy. For example, when Gallup first surveyed public opinion about the legalization of marijuana in 1969, only 12% of the public favored

Given Information: Sample 1: Sample size (n1) = 605 Out of which X = 312 said yes supporting the legalization of marijuana for medical and recreational use in the United States. Sample 2: Sample size (n2) = 635 Out of which X = 349 said yes supporting the legalization of marijuana for medical and recreational use in the United States. (a) State the hypothesis as follows: Null Hypothesis H0:p1=p2 i.e., there is no difference in the proportions who favor the legalization of marijuana. Alternative Hypothesis Ha:p1≠p2 i.e., there is a difference in the proportions who favor the legalization of marijuana. (b) Sample proportion is obtained using the formula: p^=Xn where, X is the number of successes. Sample proportion of sample 1: p^1=312605=0.5157024793≈0.5157 Sample proportion of sample 2: p^2=349635=0.5496062992≈0.5496 (c) Calculation of the test statistic: Formula: z=p^1-p^2p01-p01n1+1n2 where, p0=n1p^1+n2p^2n1+n2 Substitute the values in the formula: p0=n1p^1+n2p^2n1+n2=605×0.5157+635×0.5496605+635=311.9985+348.9961240=0.5330600806≈0.53306 Then, test statistic is obtained as follows: z=0.5157-0.54960.53311-0.53311605+1635=-0.03390.248904390.001653+0.001575=-0.03390.02835=-1.1958≈-1.19 (or) -1.20 Using a standard normal table, critical values for a two tailed test at 0.05 significance level are: -1.96 and +1.96 Since, computed value of the test statistic falls between the two critical values. In other words, since test statistic (-1.20) is greater than -1.96, we fail to reject the null hypothesis.

Answered: he Pew Research Center has reported…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Topic Video

Question

The Pew Research Center has reported results of many studies highlighting political topics and potential public policy. For example, when Gallup first surveyed public opinion about the legalization of marijuana in 1969, only 12% of the public favored legalization. A more recent survey from March 2016 showed 53% of the public favoring legalization of marijuana.

To examine potential generational differences in the proportions who favor the legalization of marijuana, researchers randomly surveyed groups of Baby Boomers (those born between 1946 and 1964) and Millennials (those born from 1981 to 1997) asking the following question: "Do you support the legalization of marijuana for medical and recreational use in the United States?"

The data were as follows.

	Yes	No	Total
Baby Boomers (population 1)	312	293	605
Millennials (population 2)	349	286	635

(a)

State the appropriate null and alternative hypotheses.

H₀: p₁

? < = > ≠

p₂

H_a: p₁

? < = > ≠

p₂

(b)

Find the value of p̂₁ and p̂₂. (Enter your answers as fractions.)

p̂₁

p̂₂

(c)

Calculate the test statistic. (Round your answer to two decimal places.)

(d)

Based on

? = 0.05,

what is the appropriate conclusion for the hypothesis test? (Use a table or SALT.)

Accept the null hypothesis.Reject the null hypothesis. Fail to reject the null hypothesis.Fail to accept the null hypothesis.

The Pew Research Center has reported results of many studies highlighting political topics and potential public policy. For example, when Gallup first surveyed public opinion about the legalization of marijuana in 1969, only 12% of the
public favored legalization. A more recent survey from March 2016 showed 53% of the public favoring legalization of marijuana.
To examine potential generational differences in the proportions who favor the legalization of marijuana, researchers randomly surveyed groups of Baby Boomers (those born between 1946 and 1964) and Millennials (those born from
1981 to 1997) asking the following question: "Do you support the legalization of marijuana for medical and recreational use in the United States?"
The data were as follows.
Yes
No
Total
Baby Boomers (population 1)
312
293
605
Millennials (population 2)
349
286
635
In USE SALT
(a) State the appropriate null and alternative hypotheses.
Ho: P, ? v
P2
? V
P2
(b) Find the value of p, and p,. (Enter your answers as fractions.)
1
P 1
P2
%D
(c) Calculate the test statistic. (Round your answer to two decimal places.)
(d) Based on a = 0.05, what is the appropriate conclusion for the hypothesis test? (Use a table or SALT.)
Accept the null hypothesis.
Reject the null hypothesis.
Fail to reject the null hypothesis.
O Fail to accept the null hypothesis.
O O

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Means$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.