Question

Make sure to include Given, Find, etc. No diagrams = no credit. Problem 1. For a normal population with known variance 2, what is the confidence level for the CI x ̅-2.14/√n≤μ≤x ̅+2.14/√n ? Problem 2. An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm. Problem 3. You are working part-time at a road construction firm. Your boss knows you are learning some statistics in your classes this semester and calls you into the office. He says, “We’ve taken sample densities from loads of asphalt we’ve gotten from our supplier. The information from their company says their process produces a consistent density with a standard deviation of 2.65 pounds per cubic foot. Here’s the data we’ve collected. Can you give me an estimate of the average density that our supplier’s process is producing? I want to be 80% confident of the range you provide.” Download the data file “CIData.txt”. Use Python or MATLAB or Excel to calculate the sample average. Problem 4. In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean number of texts handled by teens daily is given as 46 to 54. What is the standard deviation of the sample? If the number of samples were doubled, by what factor would the confidence interval change (keeping the same confidence level?) Problem 5. Hotel managers wish to learn the average length of stay of all visitors that are senior citizens. A statistician determines that for a 90% confidence level estimate of the average length of stay to within +/- 1.5 days, 65 senior visitors’ check-in/check-out records will have to be examined. How many records should be looked at to obtain a 90% confidence level estimate to within +/- 0.5 days?

Answer 1