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Chapter 7: Q. 24 (page 456)

Predict the election A polling organization plans to ask a random sample of likely voters who they plan to vote for in an upcoming election. The researchers will report the sample proportion p∧ that favors the incumbent as an estimate of the population proportion pthat favors the incumbent. Explain to someone who knows little about statistics what it means to say that p∧is an unbiased estimator of p.

Short Answer

Expert verified

The statistic is unbiased if the mean of the sample distribution of a statistic used to estimate a parameter is identical to the value of the parameter being evaluated.

Step by step solution

01

Given Information

We need to explain how sample proportion is an unbiased estimator of population proportion.

02

Explanation

The statistic is unbiased if the mean of the sample distribution of a statistic used to estimate a parameter is identical to the value of the parameter being evaluated.

An unbiased statistic will occasionally fall above and occasionally fall below the true value of a parameter if we take several samples.

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Most popular questions from this chapter

Airline passengers get heavier 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. A commuter plane carries 30 passengers. Find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds.

A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean x-x¯. Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of x-x¯will be half as big as when using a sample size of 160 . What sample size should the researcher use?

a. 40

b. 80

c. 320

d. 640

e. There is not enough information to determine the sample size.

Unemployment Each month, the Current Population Survey interviews about 60,000 randomly selected U.S. adults. One of their goals is to estimate the national unemployment rate. In October 2016,4.9% of those interviewed were unemployed.

A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that this count has mean 1.6 and standard deviation 0.75 in the population of all cars that enter at this interchange during rush hour.

a. Without doing any calculations, explain which event is more likely:

  • randomly selecting 1 car entering this interchange during rush hour and finding 2 or more people in the car
  • randomly selecting 35 cars entering this interchange during rush hour and finding an average of 2 or more people in the cars

b. Explain why you cannot use a Normal distribution to calculate the probability of the first event in part (a).

c. Calculate the probability of the second event in part (a).

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.
See all solutions

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