Question

A toy company wants to know the mean number of new toys per child bought each year. Marketing strategists at the toy company collect data from the parents of 50 randomly selected children. The sample mean is found to be 4.7 toys per child, and the sample standard deviation is calculated to be 1.5 toys per child per year.

Assume that the population standard deviation is known to be 1.9 toys per child per year. Find the error of estimate for a 90% confidence interval. Group of answer choices 0.44 0.27 0.34 0.35

Answer 1

Solution :

Given that,

Population standard deviation = = 1.9

Sample size = n = 50

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z_/2* ( /n)

= 1.645 * (1.9 / 50 )

= 0.44

The error of estimate for a 90% confidence interval is 0.44