Question

A software developer wants to know how many new computer games people buy each year. A sample of 164 people was taken to study their purchasing habits. Construct the 80% confidence interval for the mean number of computer games purchased each year if the sample mean was found to be 7.8. Assume that the population standard deviation is 1.5. Round your answers to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 7.8

Population standard deviation = = 1.5

Sample size = n = 164

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

Z/2 = Z0.10 = 1.282

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

= 1.282* (1.5 / 164 )

= 0.15

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

- E < < + E

7.8 - 0.15 < < 7.8 + 0.15

7.7 < < 8.0

(7.7 , 8.0)