07 STAT HWB q sampling

# 07 STAT HWB q sampling - Dr. V.R. Bencivenga Economics 329...

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Dr. V.R. Bencivenga Economics 329 PRACTICE ASSIGNMENT #7B: SAMPLING In each of your answers, include a description of the population, the sample statistic you are using to answer the question, its sampling distribution, and why it is valid to use this sampling distribution. Points will be deducted if this information is not included, even if your answer is otherwise correct. 1. A factory produces airplane propellers. The process it uses to produce propellers may be viewed as generating a population. The diameters of propellers it produces are approximately normally distributed, with a mean of 100 inches and a standard deviation of .02 inch. a. The factory’s manager says that 99.7% of the propellers it produces have diameters between 99.94 and 100.06 inches. Is this statement true? b. The manager’s assistant says that, if random samples each of 100 propellers are drawn from the factory’s output, the sample mean diameter will be between 99.994 and 100.006 inches in 99.7% of the samples. Is this statement true? 2. Percentage salary increases for chief executive officers of medium-sized U.S. corporations are approximately normally distributed with mean 5.5% and variance 4 (percent-squared). You take a random sample of 25 from this population. a. What is the probability that the sample mean will be between 4.987 and 6.013? b. What is the probability that the sample variance will be between 2.61 and 5.53? 3. A manager at a utility corporation predicts that January gas bills for single family homes will be approximately normally distributed with standard deviation \$35. A random sample of 25 gas bills is taken.

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## 07 STAT HWB q sampling - Dr. V.R. Bencivenga Economics 329...

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