Question

A car company believes that the percentage of students of Rutgers-Camden who owns a vehicle is 60% or less. A professor disagree with this, so she conducted a survey of 250 students and found that 166 of them own a vehicle. (a) State the null and alternative hypothesis.

(b) At α=0.025 level, is there enough evidence to support the null hypothesis.

(c) What is the p-value? (read it from the Z-table)

Answer 1

To Test :-

H0 :- P > 0.60
H1 :- P ≤ 0.60

P = X / n = 166/250 = 0.664

Test Statistic :-
Z = ( P - P0) / √(P0 * q0 / n)
Z = ( 0.664 - 0.6 ) / √(( 0.6 * 0.4) /250)
Z = 2.066

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Z(α) = Z(0.025) = 1.96
Z > -Z(α) = 2.0656 > -1.96, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is sufficient evidence to support the null hypothesis.

Part b)

P value = P ( Z < 2.0656 ) = 0.9806 ( From Z table )