Solve the problem. Round the point estimate to the nearest thousandth.

Question

Fifty people are selected randomly from a certain population and it is found that 13 people in the sample are over 6 feet tall. What is the point estimate of the proportion of people in the population who are over 6 feet tall?

A) 0.74
B) 0.26
C) 0.50
D) 0.19

Answer 1

To find the point estimate of the proportion of people in the population who are over 6 feet tall, we can use the formula for the sample proportion:

\[ \hat{p} = \frac{x}{n} \]

where:

• \( \hat{p} \) is the point estimate of the proportion,
• \( x \) is the number of successes in the sample (people over 6 feet tall),
• \( n \) is the total sample size.

From the problem:

• \( x = 13 \) (the number of people over 6 feet tall),
• \( n = 50 \) (the total number of people in the sample).

Now we can compute \( \hat{p} \):

\[ \hat{p} = \frac{13}{50} = 0.26 \]

Thus, the point estimate of the proportion of people in the population who are over 6 feet tall is \( 0.26 \).

Rounding to the nearest thousandth, we still get \( 0.260 \).

The answer is therefore:

B) 0.26