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.

A) .18
B) .622
C) .262
D) .442

Answer 1

Answer: D) 0.442

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Step-by-step explanation:

To get the point estimate, we average the endpoints of the given confidence interval. Add up the endpoints and divide by 2

(low+high)/2 = (0.262+0.622)/2 = 0.442

The value 0.442 is right in the middle of the confidence interval, so it's a natural point estimate for the population proportion.

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Alternative Method:

Subtract the endpoints to find the confidence interval width

width = high - low = 0.622 - 0.262 = 0.36

Cut this in half to get the margin of error (MoE)

MoE = width/2 = 0.36/2 = 0.18

Then we can either add on the MoE to the low endpoint, or subtract it from the high endpoint, to land on the center

• center = low + MoE = 0.262 + 0.18 = 0.442
• center = high - MoE = 0.622 - 0.18 = 0.442