Question

7. A lightbulb manufacturer wants to make sure the lightbulbs being produced give o the correct level of
brightness. Brightness is measured using the unit of measurement known as a lumen. A worker
randomly selects 100 lightbulbs and tests how bright they are. The mean brightness of this sample of
lightbulbs is 450 lumens with a standard deviation of 6.8 lumens. The worker uses this data to construct
the following 95% confidence interval: (448.67,451.33)

Answer 1

a. Interpret this confidence interval in context of the problem.
This confidence interval tells us that we can be 95% confident that the true mean brightness of all the lightbulbs produced by the manufacturer is between 448.67 and 451.33 lumens, based on the sample of 100 lightbulbs tested by the worker.

b. What is the margin of error for this confidence interval?
The margin of error for this confidence interval is (451.33 - 448.67)/2 = 1.33/2 = 0.665 lumens.

c. If the lightbulb manufacturer wants to increase the precision of their estimates, what can they do?
To increase the precision of their estimates, the lightbulb manufacturer can either increase the sample size of the lightbulbs tested or decrease the standard deviation of the brightness measurements. A larger sample size or a smaller standard deviation will result in a narrower confidence interval and therefore a more precise estimate of the true mean brightness of all the lightbulbs produced.