In a survey of a random sample of 400 people about a new bus route, 140 people said ‘yes’, 210 said ‘no’ and 50 said ‘can’t say’. The point estimate of the proportion of people in the population who would say ‘yes’ is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.35
The point estimate of a population proportion is the sample proportion: the number of ‘yes’ answers divided by the whole sample size.
\( \displaystyle \hat{p} = \frac{140}{400} \)
\(= 0.35\)
Why the other options are incorrect
Option (1) 0.40 — Incorrect. This is 140 ÷ 350, which leaves the 50 people who said ‘can’t say’ out of the sample; they are also part of the 400 people sampled.
Option (2) 0.525 — Incorrect. This is 210 ÷ 400, the proportion who said ‘no’.
Option (4) 0.60 — Incorrect. This is 210 ÷ 350, the ‘no’ proportion among only those who said ‘yes’ or ‘no’.