Question

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

H₀ : P₁− P₂ = 0.20

H_A : P₁− P₂ ≠ 0.20

x1 = 150	x2 = 130
n1 = 250	n2 = 400

a.	Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Test statistic

b.

Approximate the p-value.

	p-value < 0.01
	0.01 ≤ p-value < 0.025
	0.025 ≤ p-value < 0.05
	0.05 ≤ p-value < 0.10
	p-value ≥ 0.10

c.

At the 5% significance level, what is the conclusion?

	Reject H0; there is enough evidence to say the population proportions differ by 0.20.
	Reject H0; there is not enough evidence to say the population proportions differ by 0.20.
	Do not reject H0; there is enough evidence to say the population proportions differ by 0.20.
	Do not reject H0; there is not enough evidence to say the population proportions differ by 0.20.

d.

Using the critical value approach, can we reject the null hypothesis at the 5% level?

	Yes, since the value of the test statistic is more than the critical value of 1.645.
	No, since the value of the test statistic is more than the critical value of 1.645.
	Yes, since the value of the test statistic is less than the critical value of 1.96.
	No, since the value of the test statistic is less than the critical value of 1.96.

Answer 1

a)

value of the test statistic =1.88

b)

0.05 ≤ p-value < 0.10

c)

Do not reject H0; there is not enough evidence to say the population proportions differ by 0.20.

d)

No, since the value of the test statistic is less than the critical value of 1.96.