Question

10.

A sample of 51 observations will be taken from an infinite population. The population proportion equals 0.85. The probability that the sample proportion will be between 0.9115 and 0.946 is

Select one:

a. 0.8633

b. 0.6900

c. 0.0345

d. 0.0819

11.

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are

Select one:

a. 0.5 and 0.047

b. 500 and 0.047

c. 0.5 and 0.050

d. 500 and 0.050

Answer 1

10)

Given,

p = 0.85 , n = 51

Mean = p = 0.85

Standard deviation (SD) = Sqrt ( p( 1 - p) / n)

= Sqrt ( 0.85 * 0.15 / 51)

= 0.05

Using central limit theorem,

P( < p) = P( Z < - mean / SD)

P( 0.9115 < < 0.946) = P( < 0.946) - P( < 0.9115)

= P( Z < 0.946 - 0.85 / 0.05) - P( Z < 0.9115 - 0.85 / 0.05)

= P( Z < 1.92) - P( Z < 1.23)

= 0.9726 - 0.8907

= 0.0819

11)

Proportion of sample proportion = p = 0.5

Standard deviation of sample proportion = Sqrt( p( 1 - p) / n)

= sqrt ( 0.5 * 0.5 / 100)

= 0.05

The proportion and the standard deviation of the sample proportion is 0.5 and 0.05