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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question2answer
Answered 2021-08-16 Author has 29525 answers

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,
\(\displaystyle\hat{{{q}}}={1}-\hat{{{p}}}\)
\(\displaystyle={1}-{0.23}\)
\(\displaystyle={0.77}\)

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