Question

Independent random samples of n₁ = 800  and n₂ = 610 observations were selected from binomial populations 1 and 2, and x₁ = 336 and x₂ = 378 successes were observed.

(a) Find a 90% confidence interval for the difference (p₁ − p₂) in the two population proportions. (Round your answers to three decimal places.)

_______ to _______/

(b) What assumptions must you make for the confidence interval to be valid? (Select all that apply.)

independent random samples

symmetrical distributions for both populations

n₁ + n₂ > 1,000

np̂ > 5 for samples from both populationsnq̂ > 5 for samples from both populations

(c) Can you conclude that there is a difference in the population proportions based on the confidence interval found in part (a)?

a. Yes. Since zero is not contained in the confidence interval, the two population proportions are likely to be different.

b. No. Since zero is not contained in the confidence interval, the two population proportions are likely to be equal.    

c. No. Since zero is contained in the confidence interval, the two population proportions are likely to be equal.

d. Yes. Since zero is contained in the confidence interval, the two population proportions are likely to be different.

e. Nothing can be determined about the difference between the two population proportions.

Answer 1

a)

b) assumptions needed :

np̂ > 5 for samples from both populationsnq̂ > 5 for samples from both populations

a. Yes. Since zero is not contained in the confidence interval, the two population proportions are likely to be different.