Question

Consider the following competing hypotheses and accompanying sample data. Use Table 1.

H₀: p₁ − p₂ ≥ 0

H_A: p₁ − p₂ < 0

x1 = 236	x2 = 254
n1 = 387	n2 = 387

a.	At the 5% significance level, find the critical value(s). (Negative values should be indicated by a minus sign. Round your answer to 2 decimal places.)

Critical value

b.	Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Test statistic

c.

What is the conclusion?

	Reject H0 since the value of the test statistic is not less than the critical value.
	Reject H0 since the value of the test statistic is less than the critical value.
	Do not reject H0 since the value of the test statistic is not less than the critical value.
	Do not reject H0 since the value of the test statistic is less than the critical value.

Answer 1

H0: p1 − p2 ≥ 0

HA: p1 − p2 < 0

x1 = 236	x2 = 254
n1 = 387	n2 = 387

a)

Level of significance = 0.05

Critical value = 1.64

( From z table)

b)

Test statistic is

c)

Test statistic | z | < critical value we fail to reject null hypothsis.

Do not reject H₀ since the value of the test statistic is less than the critical value.