Question

1) suppose average pizza delivery times are normally distributed with an unknown population
mean and a population standard deviation of 6 minutes. A random sample of 28 pizza delivery
restaurants is taken and has a sample mean delivery time of 36 minutes. Find a 90% confidence
interval estimate for the population mean delivery time.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 36

Population standard deviation =    = 6
Sample size = n =28

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2    * ( /n)

= 1.645* ( 6 /  28 )

= 1.865
At 90% confidence interval estimate of the population mean
is,

- E < < + E

36-1.865 <   < 36+ 1.865

34.135 <   < 37.865