# Lecture Note 14

```ST 361: Ch 7.3 Estimation --- Interval Estimation for population proportion 
---------------------------------------------------------------------------------------------------------------------Statistical inference for  (population proportion)
 Background information (review)

The natural statistic for estimating  is ____________________________

If n is large (i.e., n  5 and n 1     5 ), the sampling distribution of p is

Because  is not known, so  p is not known. Thus p is used in the formula to calculate  p .
However, unlike before where we have to find the critical value from a t -distribution, here we
still use a Z-distribution, but this time it requires a more stringent criterion for “large n”, that
is
 Confidence interval for  : (Assume ______________________ )
The Confidence interval for  is
1
Ex. Suppose that the proportion of the left-handed students at a certain university is  . A random sample
of 200 students was collected and found that 40 out of the 200 students are left-handed.
(a) Use an unbiased estimator to compute a point estimate of  .
(b) What is the distribution of your estimator in (a)? Why?
(c) What is the standard error of your estimator?
(d) Your estimator in (a) is unbiased because (circle one) (3 points)
i. Its distribution is normal
ii. Its mean is equal to 
iii. Its SE is equal to
 1   
n
iv. It is based on a sample with size greater than 30
(e) Construct and interpret the 95% confidence interval for .
2
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