Question

A researcher believes that 9% of males smoke cigarettes.

If the researcher is correct, what is the probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by less than 3%? Round your answer to four decimal places

Answer 1

Let P : Population propertion of males smoke cigarettes. = 0.09

n= number of males in a sample = 664.

p : sample propertion of males smoke cigarettes.

The sampling distribution of propertion (p) is

p ~ N (P,PQ/n)

E(p) = P and Var(p) = PQ/n

where Q =1-P = 1-0.09 = 0.91

P ( propertion of smokers in sample of 664 males differ from the population propertion by less than 3%)

By central limit theorem

Hence

= P ( -2.7012< Z < 2.7012 )

=1 -2 * P (Z > 2.7012)

From the normal probability table

P( Z > 2.7012) = 0.0035

= 1 - 2 * 0.0035

= 0.9930

P ( propertion of smokers in sample of 664 males differ fron the population propertion by less than 3%) = 0.9930.