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

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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
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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