Question

Use the normal distribution and the given sample results to complete the test of the given...

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=______________________

Homework Answers

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

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