Question

Determine the test statistic and p-value for H₀: p = 0.2 versus H_a: p ≠ 0.2 when n = 100 and the sample proportion is 0.26.

Question 9 options:

	A. Z = 1.46; p-value = .144
	B. Z = 2.65; p-value = .008
	C, Z = 0.98; p-value = .327
	D. Z = 1.5; p-value = .134

Answer 1

To Test :-

H₀: p = 0.2

H_a: p ≠ 0.2

n = 100
P = X / n = 0.26

Test Statistic :-


Z = 1.5

Test Criteria :-
Reject null hypothesis if

= 1.5 < 1.96, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( Z > 1.5 )
P value = 0.1336
Reject null hypothesis if P value <
Since P value = 0.1336 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Option

D. Z = 1.5; p-value = .134 is correct