1.

The quality control manager at light globe factory needs to estimate the mean life of a large

shipment of energy-saving light-emitting diode (LED) light globes. The standard deviation is

3,000 hours. A random sample of 64 light globes indicates a sample mean life of 34,000 hours.

a) Construct a 95% confidence interval estimate of the population mean life of light

globes in this Shipment.

b) Do you think that the manufacturer has the right to state that the light globes last an

average of 35,000 hours? Explain.

c) Must you assume that the population of light globe life is normally distributed?

Explain.

d) Suppose that the standard deviation changes to 6,000 hours. What are your answers in

(a) and (b).

2.

Water resources in many parts of Australia are being closely watched and restrictions have

been imposed on activities such as garden watering. Suppose that Sydney Water monitors water

usage in a suburb and finds that for one summer the average household usage is 408 litres per

day. A year later it examines records of a sample of 50 households and finds that there is a

daily mean usage of 380 litres with a standard deviation of 25 litres.

a) Construct a 95% confidence interval for the population mean daily water usage in the

second summer. Assume the population usage is normally distributed.

b) interpret the interval constructed in (a)

c) Do you think water usage has changed in the second summer? Explain