**Unformatted text preview: **QUESti°n1 Suppose a random sample of size n = 100 yields 41 successes. Partially A correct The sample proportion is p: 0.41 v 7.00 points out a A of 330 A normal distribution is a good approximation for the sampling distribution of proportions if up 2 10 and n(l - p) 2 10.
V ”a“ In this example in}?! = 41 V and n(1 -j5).= 59 v/ . question When it is appropriate to approximate the distribution of sample proportions with a normal distribution, a good approximation for the standard error
(SE) for the distribution of sample proportions is given by the formula
130—13)
n . In this example the formula yields SE: 0.049 V . When it is appropriate to approximate the distribution of sample proportions with a normal distribution, a confidence interval for the population
proportion can be computed with the formula ~ Lea—.6)
p i 2* n . where z* is the standard normal endpoint for the desired level of confidence. In this example, a 90% confidence interval is 0.33 V to 0.49 -l . When it is appropriate to approximate the distribution of sample proportions with a normal distribution, we can test H0 1 p = p0 vs Ha : p 915 P0 (or
a one-tail alternative) using the standardized test statistic _ {J—Pu
z — SE where SE is given by the formula 1-
1/ P“ up”) . computed using the null proportion pg In this example, to use our sample proportion to test the null hypothesis H0 2 p = 0.5, we get test statistic z = -1.8 V with corresponding one—tailed p-value of 0.005 x . ...

View
Full Document

- Spring '08
- Watson