Question

A random sample of size n = 84 is taken from a population of size N = 931 with a population proportion p = 0.58. [You may find it useful to reference the z table.]

a-1. Is it necessary to apply the finite population correction factor?

• Yes

• No

a-2. Calculate the expected value and the standard error of the sample proportion. (Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.)

b. What is the probability that the sample proportion is less than 0.47? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Answer 1

Solution

Given that,

p = 0.58

1 - p = 1 - 0.58 = 0.42

n = 84

N = 931

a-1) No

a-2) = p = 0.58

=  [p ( 1 - p ) / n] =   [(0.58 * 0.42) / 84 ] = 0.0539

b) P( < 0.47)

= P[( - ) / < (0.47 - 0.58) / 0.0539]

= P(z < -2.04)

Using z table,

= 0.0207