Question

A random sample of 40 child residents in a large population yielded a mean weight of x= 39.2 kilograms. Suppose it is known that the distribution of weight of child residents in this population has a standard deviation of 9.8 kilograms.

A. Give an approximate 90% confidence interval for the mean weight of child residents in the population.

B. What sample size is required if we want 90% confidence and the margin of error to be 1 kilogram?

Answer 1

#Given:

n=40

=39.2

=9.8

90% confidence interval for the mean weight of child residents if    is known is

Z/2 = 1.645

(39.2-2.5,39.2+2.5)

(36.65,41.75)

#

90% confidence interval for the mean weight of child residents in the population IS (36.65,41.75)

B)

Population standard deviation = =9.8

Margin of error = E = 1

Z/2 = 1.645

sample size = n = [Z/2* / E] 2

n = [1.645 * 9.8 / 1]2

n =259.8866

Sample size = n = 260