Question

A toy manufacturer wants to know how many new toys children buy each year. A sample of 292 children was taken to study their purchasing habits. Construct the 80% 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 1.8. Round your answers to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 5.6

Population standard deviation =    = 1.8

Sample size = n =292

At 80% confidence level the z is ,

= 1 - 80 % = 1 - 0.80 = 0.20

/ 2 = 0.20/ 2 = 0.10

Z_/2 = Z_0.10= 1.28 ( Using z table ( see the 0.10 value in standard normal (z) table corresponding z value is 1.28 )

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

=1.28 * ( 1.8 /  292 )

E= 0.13
At 80% confidence interval estimate of the population mean
is,

- E < < + E

5.6 - 0.13 <   < 5.6+ 0.13

5.47 <   < 5.73

At 80% confidence interval estimate of the population mean is ( 5.5 , 5.7 )