Question

A random sample is to be selected from a population that has a proportion of successes p = 0.68. Determine the mean and standard deviation of the sampling distribution of p̂ for each of the following sample sizes. (Round your standard deviations to four decimal places.)

(a)    n = 10

standard deviation

(b)    n = 20

standard deviation

(c)    n = 30

standard deviation

(d)    n = 50

standard deviation

(e)    n = 100

standard deviation

(f)    n = 200

standard deviation

Answer 1

p=0.68 ; q= 0.32

mean = np

variance = npq

a) n=10

mean = 10 0.68 = 6.8

standard deviation = 1.4751

b) n=20

mean = 20   0.68 =13.6

standard deviation = 2.0861

c) n=30

mean = 30   0.68 = 20.4

standard deviation =2.5550

d) n=50

mean = 50   0.68 = 34

standard deviation =3.2985

e) n=100

mean = 100 0.68 = 68

standard deviation =4.6648

f) n=200

mean = 200   0.68 = 136

standard deviation =6.5970