Question

A toy manufacturer wants to know how many new toys children buy each year. A sample of 314 children was taken to study their purchasing habits. Construct the 90% confidence interval for the mean number of toys purchased each year if the sample mean was found to be 5.1. Assume that the population standard deviation is 1.31.3. Round your answers to one decimal place.

Answer 1

Solution :

Given that,
sample mean = = 5.15

Population standard deviation =   = 1.31

Sample size = n =314

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645* ( 1.31 /  314 )

=0.12
90% confidence interval for the mean
is,

- E < < + E

5.15-0.12 <    < 5.15 + 0.12

5.03 <   < 5.27

( 5.03 , 5.3) (ROUNDED )

90% confidence interval for the mean number of toys purchased each year ( 5.0 , 5.3)