# need help stats

• Jul 8th 2007, 02:51 AM
harry
need help stats
Confidence interval for a population proportion.
In a random sample of 400 students at a university, 332 stated that they were nonsmokers. Based on this sample, compute a 95% confidence interval for the proportion of all students at the university who are nonsmokers. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places
(a)What is the lower limit of the confidence interval?
(b) What is the upper limit of the confidence interval?
• Jul 8th 2007, 04:58 AM
rualin
Confidence interval for the population proportion: $\hat{P} - E < p < \hat{P} + E$, where $E = z_c \sqrt{\frac{\hat{p} \cdot \hat{q}}{n}}$.

Make a list of the given information for easier reference.
$n=400$
$x=332$
$c=95\%=0.95$
$z_c=1.96$ by looking at the standard normal distribution table
$\hat{p} = \frac{x}{n} = \frac{332}{400} = 0.83$
$\hat{q} = 1 - \hat{p} = 1 - 0.83 = 0.17$

Solving for E, we get:
$E = 1.96 \sqrt{\frac{0.83 \cdot 0.17}{400}} \approx 0.0368$

And substituting back into the confidence interval formula:
$0.83 - 0.0368 < p < 0.83 + 0.0368$
$\boxed{0.793 < p < 0.867}$
• Jul 8th 2007, 06:38 AM
CaptainBlack
Quote:

Originally Posted by harry
Confidence interval for a population proportion.
In a random sample of 400 students at a university, 332 stated that they were nonsmokers. Based on this sample, compute a 95% confidence interval for the proportion of all students at the university who are nonsmokers. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places
(a)What is the lower limit of the confidence interval?
(b) What is the upper limit of the confidence interval?

Just to be arkward I will observe that you cannot get such a confidence
interval using this data. A significant number of respondents lied, giving
the answer that they thought would make them look good in the eyes
of the survey organisers.

All you can do is obtain a 95% confidence interval for the proportion of
students at the university who would have claimed to be non-smokers
on a survey worded and conducted like the one in question.

RonL