Question

A new beta-blocker medication is being tested to treat high blood pressure. Subjects with high blood pressure volunteered to take part in the experiment. 160 subjects were randomly assigned to receive a placebo and 210 received the medicine. High blood pressure disappeared in 100 of the controls and in 112 of the treatment group. Test the claim that the new beta-blocker medicine is effective at a significance level of αα = 0.05.

What are the correct hypotheses?

H0: Select an answerσ₁x̅₂x̅₁pp₁μ₁μ₂p₂ ?≤<≥>≠= Select an answerp₂x̅₂pp₁σ₂μ₁0x̅₁μ₂

H1: Select an answerp₂x̅₂p₁σ₁x̅₁μ₂μ₁p ?>=≤≠<≥ Select an answer0σ₁x̅₂x̅₁μ₂μ₁p₁pp₂

Based on the hypotheses, find the following:

Test Statistic =

p-value =

The test statistic is: Select an answerin the critical regionnot in the critical region .

The correct decision is to Select an answeraccept the null hypothesisreject the claimreject the null hypothesisaccept the alternative hypothesisfail to reject the null hypothesis .

The correct summary would be: Select an answerThere is enough evidence to supportThere is not enough evidence to rejectThere is enough evidence to rejectThere is not enough evidence to support the claim that the new beta-blocker medicine is effective at a significance level of αα = 0.05.

Answer 1

Sample 1:

n1 = 160, x1 = 100

p̂1 = x1/n1 = 0.625

Sample 2:

n2 = 210, x2 = 112

p̂2 = x2/n2 = 0.5333

α = 0.05

Null and Alternative hypothesis:

Ho : p1 ≤ p2

H1 : p1 > p2

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (100+112)/(160+210) = 0.573

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.625 - 0.5333)/√[0.573*0.427*(1/160+1/210)] = 1.7660

p-value = 1- NORM.S.DIST(1.766, 1) = 0.0387

The test statistic is: in the critical region.

The correct decision is to : reject the null hypothesis

The correct summary would be: There is enough evidence to support the claim that the new beta-blocker medicine is effective at a significance level of α = 0.05.