Question

Suppose we wish to conduct a survey to find p, the proportion of 1st year undergraduate students who hope to attend graduate school. We'd like to be able to create a 94% confidence interval that it has a length of 0.1 (i.e. L=0.1). How many students do we need to sample if a pilot study shows that the sample proportion is 0.2? Select one: O a. 237 O b. 254 | 0 227 o ooo d. 244 e. 254 f. 354 g. 277 O

Answer 1

We have given,
Preliminary estimate for proportion (Known) = 0.2
Margin of error =E=0.1/2=0.05....margin of error is half of the length of confidence interval
Level of significance =   1-0.94=0.06
Z critical value is (by using Z table) =1.881
Sample size formula is                   

n = [p(1-P)]

$=\left [ 0.20 (1-0.20)\right ]\left [ \frac{1.881}{0.05} \right ]^2$
=226.44

c) 227