08 STAT HWB q estimation - Dr. V.R. Bencivenga Economics...

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Dr. V.R. Bencivenga Economics 329 PRACTICE ASSIGNMENT #8B: ESTIMATION For each question, include as part of your answer the sampling distribution of the estimator, and the reason(s) why this sampling distribution is valid. 1. The admissions office of an MBA program knows from historical experience that applicants have GPA’s that are approximately normally distributed with standard deviation .25. A random sample of 25 applications from the current year has a sample mean GPA of 3.1. Find the 95% confidence interval for the population mean. 2. A quality control person wants to estimate the mean output voltage of a certain type of electrical power supply unit. Output voltage is approximately normally distributed, with a variance of 9 squared volts, in units of this type. She tests a random sample of 10 units, and the mean is 110.5 in this sample. a. Calculate a two-sided 95% confidence interval. b. Suppose the only concern is that too low a mean would result in equipment malfunction. Compute the appropriate one-sided 95% confidence interval. c. Suppose instead the only concern is that too high a mean would result in equipment malfunction. Compute the appropriate one-sided 95% confidence interval in this case. 3. Airlines use sampling to estimate the mean amount of revenue they receive for passengers traveling on more than one airline. Suppose an airline’s revenue from multi -airline passengers is approximately normally distributed with variance 2500 (squared dollars). The airline wants to estimate the mean of this normal distribution to within $5 dollars (i.e., plus or minus $5) with a confidence level of 99%. What is the smallest sample size the airline can use? 4. A lake pollution study measures the concentration of lead in 25 sediment samples from the upper sedimentary layer of the lake. The sample mean concentration is .38 parts per thousand, and the sample standard deviation is .06 parts per thousand. Assuming that concentrations of lead at different points are approximately normally distributed, compute the 95% confidence interval for the population mean concentration of lead. 5. A drug firm attempts to estimate the extent to which a new enzyme has altered the yield of a certain manufacturing process. Yield is measured by the ratio of output using the new enzyme to theoretical output based on formulas describing the old process. A yield of 1.03 indicates
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08 STAT HWB q estimation - Dr. V.R. Bencivenga Economics...

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