Question

A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 95% confidence interval for the proportion of college students who prefer drink A: (.262, .622). Identify the point estimate for estimating the true proportion of college students who prefer that drink.

Answer 1

The point estimate for the proportion of college students who prefer drink A is found by averaging the lower and upper bounds of the 95% confidence interval, which yields an estimate of 0.442 or 44.2%.

Step-by-step explanation:

The point estimate for the true proportion of college students who prefer drink A is the midpoint of the 95% confidence interval. To find the point estimate, you sum the lower and upper bounds of the interval and divide by 2. In this case, the confidence interval is (.262, .622). The calculation for the point estimate is (0.262 + 0.622) / 2, which equals 0.442. Therefore, the point estimate is 0.442, which means that approximately 44.2% of college students prefer drink A.

Answer 2

The point estimate for estimating the true proportion of college students who prefer that drink is 0.462.

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

The point estimate for the true proportion is the midpoint between these two bounds, that is, the lower bound added to the upper bound, and divided by 2.

In this problem, we have that:

Lower bound: 0.262

Upper bound: 0.662

Identify the point estimate for estimating the true proportion of college students who prefer that drink.

p = (0.262 + 0.662)/2 = 0.462

The point estimate for estimating the true proportion of college students who prefer that drink is 0.462.