Two different simple random samples are drawn from two different populations. Th

Question

Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 16 having a common attribute. The second sample consists of 2000 people with 1458 of them having the same common attribute. Compare the results from a hypothesis test of p1 = p2 (with a .05 significance level) and a 95% confidence interval estimate of p1 p2.

What are the null and alternative hypotheses for the hypothesis test?
Identify the test statistic. (round to two decimal places as needed)
Identify the critical value(s). (round to three decimal places as needed)
What is the conclusion based on the hypothesis test?
The test statistic is () the critical region, so () the null hypothesis. There is () evidence to conclude that p1 p2.
The 95% confidence interval is () < (p1 - p 2) < () (round to three decimal places as needed)
What is the conclusion based on the confidence interval?
Since 0 is () in the interval, it indicates to () the null hypothesis.
How do the results from the hypothesis test and the confidence interval compare?
The results are (), since the hypothesis test suggests that p1 () p2, and the confidence interval suggests that p1 () p2.

Explanation / Answer

Solution:

Given that x1 = 16, x2 = 1458

n1 = 30, p1 = 16/30 = 0.5
n2 = 2000, p2 = 1458/2000 = 0.729

The test hypothesis is
H0:p1=p2
Ha:p1 p2

The test statistic is
Z = (p1-p2)/[p1*(1-p1)/n1 +p2*(1-p2)/n2]

= (0.5-0.729)/sqrt(0.5*0.5/30 + 0.729*(1-0.729)/2000)

= -2.4938

Given = 0.05, the critical value is Z(0.025) = -1.96 (check standard normal table)

Since Z = -2.4938 is larger than -1.96, we do not reject Ho.

The 95% CI is

CI = (p1-p2) ± Z*[p1*(1-p1)/n1 +p2*(1-p2)/n2]

= (0.5-0.729) ± 1.96*sqrt(0.5*0.5/30 + 0.729*(1-0.729)/2000)

= (-0.4089, -0.0490)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.