For questions 1and 2, identify the population and sample. Then state whether the boldface number is a parameter or a statistic and use appropriate notation to describe each number; for example, p = 0.65.
1.
A large container is full of ball bearings with mean diameter 2.5003
cm. This is within the specifications for acceptance of the container by the purchaser. By chance, an inspector chooses 100 bearings from the container that have mean diameter 2.5009
cm. Because this is outside the specified limits, the container is mistakenly rejected.
2.
A telemarketing firm in a large city uses a device that dials residential telephone numbers in that city at random. Of the first 100 numbers dialed, 48% are unlisted. This is not surprising because 52% of all residential phones in the city are unlisted.
3.
A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13- to 16year-olds. a.
The researchers will report the mean x from their sample as an estimate of the mean cholesterol level μ in this population. Explain to someone who knows little about statistics what it means to say that x is an unbiased estimator of
μ
. b.
The sample mean x is an unbiased estimator of the population mean
μ
no matter what size SRS the study chooses. Explain to someone who knows nothing about statistics why a large random sample will give more trustworthy results than a small random sample.

4.
A USA Today Poll asked a random sample of 1012 U.S. adults what they do with the milk in the bowl after they have eaten the cereal. Let p be the proportion of people in the sample who drink the cereal milk. A spokesman for the dairy industry claims that 70% of all U.S. adults drink the cereal milk. Suppose this claim is true. a.
What is the mean of the sampling distribution of p ? Why? b.
Find the standard deviation of the sampling distribution of p . Check to see if the 10% condition is met. c.
Is the sampling distribution of p approximately Normal? Check to see if the Large Counts condition is met. d.
Of the poll respondents, 67% said that they drink the cereal milk. Find the probability of obtaining a sample of 1012 adults in which 67% or more, P(X ≥ 0.67), say they drink the cereal milk if the milk industry spokesman’s claim is true. e.
Does this poll give convincing evidence against the claim? Explain.
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5.
David’s iPod has about 10,000 songs. The distribution of the play times for these songs has a mean of
225 seconds and a standard deviation of 60 seconds. Suppose we choose an SRS of 10 songs from this population and calculate the mean play time x of these songs. What are the mean and the standard deviation of the sampling distribution of x ? Explain.
6.
In response to the increasing weight of airline passengers, the Federal Aviation
Administration (FAA) told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. Weights are not Normally distributed, especially when the population includes both men and women, but they are not very non-Normal. A commuter plane carries 30 passengers. a.
Is the sampling distribution approximately Normal? Use the Central Limit Theorem to justify your response. b.
Calculate the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds. Show your work. ( Hint : Restate the problem in terms of the mean weight.)
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