Homework Confidence Interval #1

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

  1. 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.
    1. Set up a 95 percent confidence interval estimate of the true average life of light bulbs in this shipment.
    2. What critical value was used in calculating this interval?
    3. What is the 95 percent margin of error for this estimate?
    4. What sample size is needed to reduce the 95 percent margin of error to 10 hours?

     

  2. 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.
    1. Set up a 95 percent confidence interval estimate of the true average amount of soft drink in each bottle.
    2. What is the 95 percent margin of error for this estimate?
    3. What sample size would be needed if only a 90 percent confidence interval estimate with a margin of error of 0.0098 was desired?
    4. What critical value would be used to calculate a 90 percent confidence interval?