### Homework Confidence Interval #1

#### Complete the two problems below using the FORMULAS
on the Confidence Interval Chart. Show ALL work.

- The quality control manager at a light bulb factory needs to estimate
the average life of a large shipment of light bulbs. The
process standard deviation is known to be 100 hours. A random sample
of 64 light bulbs indicate a sample average life of 350 hours.
- Set up a 95 percent confidence interval estimate of the true
average life of light bulbs in this shipment.
- What critical value was used in calculating this interval?
- What is the 95 percent margin of error for this estimate?
- What sample size is needed to reduce the 95 percent margin of error
to 10 hours?

- The inspection division of the Lee County Weights and Measures Department
is interested in estimating the actual amount of soft drink that is placed in
2-liter bottles at the local bottling plant of a nationally known soft-drink
company. The bottling plant has informed the inspection division that
the standard deviation for 2-liter bottle is 0.05 liter. A random
sample of one hundred 2-liter bottles obtained from this bottling plant
indicates a sample average of 1.99 liters.
- Set up a 95 percent confidence interval estimate of the true
average amount of soft drink in each bottle.
- What is the 95 percent margin of error for this estimate?
- What sample size would be needed if only a 90 percent confidence
interval estimate with a margin of error of 0.0098 was desired?
- What critical value would be used to calculate a 90 percent
confidence interval?