Independent random samples of n₁ = 800  andn₂ = 610 observations were selected from binomialpopulations 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 twopopulation proportions. (Round your answers to three decimalplaces.)

_______ to _______/

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

independent random samples

symmetrical distributions for both populations

n₁ + n₂ > 1,000

np̂ > 5 for samples from bothpopulationsnq̂ > 5 for samples from bothpopulations

(c) Can you conclude that there is a difference in thepopulation proportions based on the confidence interval found inpart (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 beequal.    

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

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

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