Question

A toy manufacturer wants to know how many new toys children buy each year. A sample of 499 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 5.6. Assume that the population standard deviation is 1.9.

Answer 1

Solution :

Given that,

= 62.5

= 8.8

n = 499

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/ 499 )

= 0.14

At 90% confidence interval estimate of the population mean is,

- E < < + E

5.6 - 0.14 < < 5.6 + 0.14

5.46 < < 5.74

(5.46 ,5.74)