Assessment Part 2

Question

An online grocery company is researching the best location to start their new delivery service. They are comparing two local regions, A and B. In a random sample of 505 residents in region A, 26.1% said that they would use an online grocery store. In a random sample of 388 residents in region B, 29.5% said they would use an online grocery store.

Find a 95% confidence interval for the difference in the proportions of residents in these two regions who would use an online grocery store.

The CEO believes that region B will have a higher proportion of potential customers than region A. Does your confidence interval support that conclusion? Explain.

Answer 1

phat1 = 0.261

phat2 = 0.295

n1 = 505

n2 = 388

z-critical for 95% CI is 1.96

CI = (phat2 - phat1) +/- z-critical * sqrt(phat1*(1-phat1)/n1 + phat2(1-phat2)/n2)

(0.295 - 0.261) +/- 1.96 * sqrt(0.261*0.739/505 + 0.295*0.705/388)

-0.025,0.093

Since the CI contains 0 as a plausible difference between proportions, it is possible to have those proportions differ by the amount in the samples by chance, however, the CI is skewed towards a positive difference, which would lead one B has a higher proportion though not a statistically significant higher proportion.