Question

I conducted a survey and found 86 out of 150 preferred riding with their significant other compared to 44 out of 100 women who preferred to ride their own motorcycle. Does my random sampling determine if lady riders prefer riding with their significant other over riding alone at α = 0.04 level?

My Hypotheses are:

Hο: p1 ≥ p2

HA: p1 > p2

My Problem

Together: Alone:

Riders, x: 86 44

Sample Size, n: 150 100

Answer 1

To Test :-

H0 :- P1 P2

H1 :- P1 > P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 86 + 44 ) / ( 150 + 100 )
= 0.52

Z = 2.07

Test Criteria :-
Reject null hypothesis if

= 2.07 > 1.75, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z > 2.07 )
P value = 0.0192
Reject null hypothesis if P value <
Since P value = 0.0192 < 0.04, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that lady riders prefer riding with their significant other over riding alone at α = 0.04 level of significance.