Question

A food-research and consulting firm reported in 2013 that 54% of Americans prefer hot or spicy foods and sauces. Suppose that a condiment company is considering expansion of its dipping sauce product line with a new spicy flavor. The company requested its marketing research vendor to conduct a large-scale study to test whether consumer taste preference for spicy flavoring has increased since 2013. The marketing research vendor surveyed 2550 randomly selected adult Americans from its national consumer panel and found that 1428 prefer spicy flavoring.

(a) Find and interpret the 95% confidence interval for the proportion of adults that prefers spicy foods and sauces.

Answer 1

Solution :

Given that,

n = 2550

x = 1428

Point estimate = sample proportion = = x / n = 1428 / 2550 = 0.560

1 - = 0.440

Z_/2 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.560 * 0.440) / 2550)

= 0.019

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.560 - 0.019 < p < 0.560 + 0.019

0.541 < p < 0.579

(0.541 , 0.579)