Question

Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random sample and use a 5% significance level.

Test H0 : p = 0.25 vs Ha : p < 0.25 using the sample results p^ = 0.16 with n = 100

Round your answer for the test statistic to two decimal places, and your answer for the p-value to three decimal places.

test statistic=________________________

p-value=______________________

Answer 1

P0 = 0.25
q0 = 1 - P0 = 0.75
n = 100
P = X / n = 16/100 = 0.16

Test Statistic :-
Z = ( P - P0) / √(P0 * q0 / n)
Z = ( 0.16 - 0.25 ) / √(( 0.25 * 0.75) /100)
Z = -2.08

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Z(α) = Z(0.05) = 1.6449
Z < -Z(α) = -2.0785 < -1.6449, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z < -2.0785 )
P value = 0.019
Reject null hypothesis if P value < α = 0.05
Since P value = 0.0188 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0