Question

A simple random sample of 85 students is taken from a large university on the West Coast to estimate the proportion of students whose parents bought a car for them when they left for college. When interviewed, 51 students in the sample responded that their parents bought them a car. What is a 95% confidence interval for p, the population proportion of students whose parents bought a car for them when they left for college

Answer 1

Answer:

95% confidence interval for p, the population proportion of students whose parents bought a car for them when they left for college

(0.4958 , 0.7041)

Step-by-step explanation:

Step(i):-

Given that the sample size 'n' = 85

The sample proportion

            $p = \frac{x}{n} = \frac{51}{85} = 0.6$

95% confidence interval for p, the population proportion of students whose parents bought a car for them when they left for college

$(p^{-} -Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} +Z_{0.05} \sqrt{\frac{p(1-p)}{n} })$

Step(ii):-

Given that the level of significance

α = 0.05

Z₀.₀₅ = 1.96

$(0.6 -1.96 \sqrt{\frac{06(1-06)}{85} } , 0.6 +1.96 \sqrt{\frac{0.6(1-0.6)}{85} })$

(0.6 - 0.104138 , 0.6 +0.104138)

(0.4958 , 0.7041)

Final answer:-

95% confidence interval for p, the population proportion of students whose parents bought a car for them when they left for college

(0.4958 , 0.7041)