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Chapter 5: Q14E (page 307)
Question: Refer to Exercise 5.5, in which we found the sampling distribution of the sample median. Is the median an unbiased estimator of the population mean m?
Yes, the median is an unbiased estimator of the population mean 鈥渕鈥�.
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Question:A random sample of 40 observations is to be drawn from a large population of measurements. It is known that 30% of the measurements in the population are 1s, 20% are 2s, 20% are 3s, and 30% are 4s.
a. Give the mean and standard deviation of the (repeated) sampling distribution of, the sample mean of the 40 observations.
b. Describe the shape of the sampling distribution of. Does youranswer depend on the sample size?
Plastic fill process. University of Louisville operators examined the process of filling plastic pouches of dry blended biscuit mix (Quality Engineering, Vol. 91, 1996). The current fill mean of the process is set at = 406 grams, and the process fills standard deviation is = 10.1 grams. (According to the operators, 鈥淭he high level of variation is since the product has poor flow properties and is, therefore, difficult to fill consistently from pouch to pouch.鈥�) Operators monitor the process by randomly sampling 36 pouches each day and measuring the amount of biscuit mix in each. Consider the mean fill amount of the sample of 36 products. Suppose that on one particular day, the operators observe = 400.8. One of the operators believes that this indicates that the true process fill mean for that day is less than 406 grams. Another operator argues that = 406, and the small observed value is due to random variation in the fill process. Which operator do you agree with? Why?
Purchasing decision. A building contractor has decided to purchase a load of the factory-reject aluminum siding as long as the average number of flaws per piece of siding in a sample of size 35 from the factory's reject pile is 2.1 or less. If it is known that the number of flaws per piece of siding in the factory's reject pile has a Poisson probability distribution with a mean of 2.5, find the approximate probability that the contractor will not purchase a load of siding
Soft-drink bottles. A soft-drink bottler purchases glass bottles from a vendor. The bottles are required to have an internal pressure of at least 150 pounds per square inch (psi). A prospective bottle vendor claims that its production process yields bottles with a mean internal pressure of 157 psi and a standard deviation of 3 psi. The bottler strikes an agreement with the vendor that permits the bottler to sample from the vendor鈥檚 production process to verify the vendor鈥檚 claim. The bottler randomly selects 40 bottles from the last 10,000 produced, measures the internal pressure of each, and finds the mean pressure for the sample to be 1.3 psi below the process mean cited by the vendor.
a. Assuming the vendor鈥檚 claim to be true, what is the probability of obtaining a sample mean this far or farther below the process mean? What does your answer suggest about the validity of the vendor鈥檚 claim?
b. If the process standard deviation were 3 psi as claimed by the vendor, but the mean were 156 psi, would the observed sample result be more or less likely than in part a? What if the mean were 158 psi?
c. If the process mean were 157 psi as claimed, but the process standard deviation were 2 psi, would the sample result be more or less likely than in part a? What if instead the standard deviation were 6 psi?
Question:A random sample of n = 500 observations is selected from a binomial population with p = .35.
a. Give the mean and standard deviation of the (repeated) sampling distribution ofthe sample proportion of successes for the 500 observations.
b. Describe the shape of the sampling distribution of . Does your answer depend on the sample size?
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