Among college students, the proportion p who say they're interested in their congressional district's election results has traditionally been 75%. After a series of debates on campuses, a political scientist claims that the proportion of college students who say they're interested in their district's election results is more than 75%. A poll is commissioned, and 217 out of a random sample of 265 college students say they're interested in their district's election results. Is there enough evidence to support the political scientist's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H :O H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal places.) (e) Is there enough evidence to support the political scientist's claim that the proportion of college students who say they're interested in their district's election results is more than 75%2 H Ix X 7 O X S 2 0=0 OSO Р

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
Among college students, the proportion p who say they're interested in their congressional district's election results has traditionally been 75%. After a series of
debates on campuses, a political scientist claims that the proportion of college students who say they're interested in their district's election results is more than
75%. A poll is commissioned, and 217 out of a random sample of 265 college students say they're interested in their district's election results. Is there enough
evidence to support the political scientist's claim at the 0.05 level of significance?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis H and the alternative hypothesis H₁.
H₁ :0
H₁ :0
(b) Determine the type of test statistic to use.
(Choose one) ▼
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the critical value. (Round to three or more decimal places.)
0
(e) Is there enough evidence to support the political scientist's claim that the
proportion of college students who say they're interested in their district's
election results is more than 75%²
Explanation
Check
OL
I
3
|x
KLL
X
ㅁㅁ
#
X
S
0-
O<O
Cad
р
OSO 020
<P
Ś
8
0>0
2022 McGraw Hill LLC. All Rights Reserved. Terms of Use
Privacy Center
A
Transcribed Image Text:Among college students, the proportion p who say they're interested in their congressional district's election results has traditionally been 75%. After a series of debates on campuses, a political scientist claims that the proportion of college students who say they're interested in their district's election results is more than 75%. A poll is commissioned, and 217 out of a random sample of 265 college students say they're interested in their district's election results. Is there enough evidence to support the political scientist's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. H₁ :0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal places.) 0 (e) Is there enough evidence to support the political scientist's claim that the proportion of college students who say they're interested in their district's election results is more than 75%² Explanation Check OL I 3 |x KLL X ㅁㅁ # X S 0- O<O Cad р OSO 020 <P Ś 8 0>0 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center A
Expert Solution
Step 1

A) first of all we have to construct null and alternative hypotheses as follows
we know that null hypothesis always contain sign ≤, ≥,=
and alternative hypothesis always contain sign <,>,≠
the alternative hypothesis contains opposite sign to null hypothesis
Null and alternative hypothesis can be stated as follows :-
H0: p= 0.75

H1:p>0.75 (test is right-tailed)

b)z test statistic, because sampling distribution of proportion follows normal distribution with mean equal to population parameter p and standard deviation given by formula √(p(1-p)/n)

 

c) Next step is to find test statistic, formula for test statistics

test statistic z =(p^−p)/√(pq) /n
Where
p^=x/n
where x are favorable outcomes corresponding to sample data
n is total sample size taken

p^  =   217
   265


p^ = 0.8188679245283

Calculate our test statistic z:

z  =   p^ - p
   p(1 - p)/n

 

z  =   0.81887- 0.75
   0.75(1 - 0.75)/265

 

z  =   0.06887
   0.75(0.25)/265

 

z  =   0.06887
   0.000708

 

z  =   0.068867924528302
   0.026599758829947


z = 2.589

steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman