# Based on a simple random sample of 1300 college students, it is found that 299 students own a car. We wish to construct a 90\% confidence interval to estimate the proportions of all college students who own a car.

UkusakazaL 2021-08-08

Based on a simple random sample of 1300 college students, it is found that 299 students own a car. We wish to construct a $$\displaystyle{90}\%$$ confidence interval to estimate the proportions ? of all college students who own a car.
A) Read carefully the text and provide each of the following:
The sample size $$\displaystyle?=$$
from the sample, the number of college students who own a car is $$\displaystyle?=$$
the confidence level is $$\displaystyle{C}{L}=$$ $$\displaystyle\%$$.
B) Find the sample proportion $$\displaystyle\hat{{?}}=$$
and $$\displaystyle\hat{{?}}={1}−\hat{{?}}=$$

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Step 1
(A)
The sample size is, $$\displaystyle{n}={1300}$$
The number of college students who own a car is,
$$\displaystyle{x}={299}$$
The confidence level is, $$\displaystyle{C}{L}={90}\%$$
Step 2
(B)
The value of sample proportion is,
$$\displaystyle\hat{{{p}}}={\frac{{{x}}}{{{n}}}}$$
$$\displaystyle={\frac{{{299}}}{{{1300}}}}$$
$$\displaystyle={0.23}$$
The value of $$\displaystyle\hat{{{1}}}$$ is,
$$\displaystyle\hat{{{q}}}={1}-\hat{{{p}}}$$
$$\displaystyle={1}-{0.23}$$
$$\displaystyle={0.77}$$