Question

Fisher-Price wants to know the mean number of new toys bought per child each year. Marketing strategists at the toy company collect data from the parents of 1842 randomly selected children. The sample mean is found to be 4.7 toys per child. Construct a 95% confidence interval for the mean number of new toys per child purchased each year. Assume that the population standard deviation is known to be 1.9 toys per child per year.  

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 4.7

Population standard deviation =    = 1.9

Sample size n =1842

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96* (1.9 / 1842)

= 0.087
At 95% confidence interval mean
is,

- E < < + E

4.7 - 0.087 <   < 4.7 + 0.087

4.613 <   < 4.787