Question

NEED ANSWER WITHIN AN HOUR

a. For the cases below, calculate the standard error for estimate of the proportion? n = 500 and p = 0.1 n = 100 and p = 0.92

b. Comment on whether the sample sizes are large enough so that the sample proportions can be approximated by a normal distribution

Answer 1

a. 1.) When n= 500 and p=0.1. Standard error for the estimated the proportion p = √ (p(1-p)/n

= √ [0.1 (1-0.1)/500]

= 0.0134

2.) When n = 100 and p =0.92, Standard error for the estimated the proportion p = √ (p(1-p)/n

= √ [0.92 (1-0.92)/100]

= 0.027

b.) Yes, sample size are large enough for the sample proportions to be approximated via normal distribution. As a rule of thumb, the sample size must be greater than 30 and it is true in this example.

Also, we should have np > 5 and n(1-p) > 5

For our example the conditions stated above are true.