Parameters Statistics Biased Unbiased

The statistic x̅ is used as an estimator for which of the following?

• n

• s

• z

The distribution of prices for a certain car model is approximately normal with mean $21,800 and standard deviation $400. A random sample of 4 cars of the model will be selected. What is the correct unit of measure for the mean of the sampling distribution of x̅ ?

• Dollars

• Models

• Cars

• Samples

• There are no units associated with the mean of the sampling distribution.

The histograms show the results of three simulations of a sampling distribution of a sample mean. For each simulation, 1,500 samples of size n were selected from the same population and the sample mean was recorded. The value of n was different for each of the three simulations.

Which of the following is the correct ordering of the graphs from least value of n to greatest value of n ?

• A, C, B

• B, A, C

• B, C, A

• C, A, B

• C, B, A

A certain statistic will be used as an unbiased estimator of a parameter.

Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.

Which of the following must be true about

J and K ?

• The expected value of J will be equal to the expected value of K, and the variability of J will be equal to the variability of K

• The expected value of J will be greater than the expected value of K, and the variability of J will be greater than the variability of K.

• The expected value of J will be greater than the expected value of K, and the variability of J will be less than the variability of K.

• The expected values of J and K will be equal, and the variability of J will equal the variability of K.

• The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

The following graphs show the sampling distributions for two different point estimators, R and W, of the same population parameter.

Which of the following statements is true?

• Both R and W are unbiased.

• R is biased, and W is unbiased

• Both R and W are biased.

• R is unbiased, and W is biased.

• The assessment of bias is not possible, because the sampling distributions display too much variability.

A recent report indicated that 22 percent of the households in a certain community speak a language other than English at home. A reporter will randomly select a household from the community until the first household that speaks a language other than English at home is selected. Let random variable Q represent the number of attempts needed until the first household that speaks a language other than English at home is selected. The random variable Q has a geometric distribution with p=0.22.

Which of the following is closest to the variance of the random variable?

• 0.0484

• 3.5454

• 4.0144

• 4.5455

• 16.1157

The random variable W has a geometric distribution with p=0.25. Approximately how far do the values of W typically vary, on average, from the mean of the distribution?

• 1.73

• 2.00

• 3.00

• 3.46

• 4.00