Question

Generally speaking, would you say that most people can be trusted? A random sample of n1 = 255 people in Chicago ages 18-25 showed that r1 = 43 said yes. Another random sample of n2 = 270 people in Chicago ages 35-45 showed that r2 = 65 said yes. Does this indicate that the population proportion of trusting people in Chicago is higher for the older group? Use α = 0.05.

a)What is the value of the sample test statistic? (Test the difference p₁ − p₂. Do not use rounded values. Round your final answer to two decimal places.)

b) Find (or estimate) the P-value. (Round your answer to four decimal places.

Answer 1

P1 :- Proportion of people in Chicago ages 18-25

P2 :- Proportion of people in Chicago ages 35-45

To Test :-

H0 :- P1 = p2

H1 :- P1 < P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 43 + 65 ) / ( 255 + 270 )
= 0.2057

Z = -2.04

Test Criteria :-
Reject null hypothesis if

= -2.04 < -1.64, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z < -2.04 )
P value = 0.0207
Reject null hypothesis if P value <
Since P value = 0.0207 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that the population proportion of trusting people in Chicago is higher for the older group at 5% level of significance.