Chapter 7 Multiple Choice Test Review

Following a dramatic drop of 500 points in the Dow Jones Industrial Average in September 1998, a poll conducted for the Associated Press found that 92% of those polled said that a year from now their family financial situation will be as good as it is today or better. The number 92% is a

• (a) Statistic

• (b) Sample

• (c) Parameter

• (d) Population

• (e) None of the above

In a large population, 46% of the households own VCRs. A simple random sample of 100 households is to be contacted and the sample proportion computed. The mean of the sampling distribution of the sample proportion is

• (a) 46

• (b) 0.46

• (c) about 0.46, but not exactly 0.46

• (d) 0.00248

• (e) the answer cannot be computed from the information given.

If a population has a standard deviation σ, then the standard deviation of the mean of 100 randomly selected items from this population is

• (a) σ

• (b) 100 σ

• (c) σ /10

• (d) σ /100

• (e) 0.1

The distribution of values taken by a statistic in all possible samples of the same size from the same population is

• (a) the probability that the statistic is obtained.

• (b) the population parameter.

• (c) the variance of the values.

• (d) the sampling distribution of the statistic.

• (e) none of the above.

If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated, the statistic is said to be

• (a) random

• (b) biased

• (c) a proportion

• (d) unbiased

• (e) none of the above.

The central limit theorem is important in statistics because it allows us to use the Normal distribution to make inferences concerning the population mean:

• (a) provided that the sample size is reasonably large (for any population).

• (b) provided that the population is Normally distributed and the sample size is reasonably large.

• (c) provided that the population is Normally distributed (for any sample size).

• (d) provided that the population is Normally distributed and the population variance is known (for any sample size).

• (e) provided that the population size is reasonably large (whether the population distribution is known or not).

A simple random sample of 1000 Americans found that 61% were satisfied with the service provided by the dealer from which they bought their car. A simple random sample of 1000 Canadians found that 58% were satisfied with the service provided by the dealer from which they bought their car. The sampling variability associated with these statistics is

• exactly the same.

• smaller for the sample of Canadians because the population of Canada is smaller than that of the United States, hence the sample is a larger proportion of the population.

• smaller for the sample of Canadians because the percent satisfied was smaller than that for the Americans.

• larger for the Canadians because Canadian citizens are more widely dispersed throughout the country than in the United States, hence they have more variable views.

• about the same.

An SRS of n₁ = 100 is selected from population 1, which follows a Normal distribution with a mean of 40 and a standard deviation of 4. An independent SRS of n₂ = 85 is selected from population 2, which follows a Normal distribution with a mean of 25 and a standard deviation of 7. Which of the following expressions represents the standard deviation of the sampling distribution of x̄₁ - x̄₂?

• (a)

• (b)

• (c)

• (d)

• (e)

According to the Humane Society, 39% of households in the United States have at least one dog. In the United Kingdom, 23% of households have at least one dog. Suppose you select an SRS of 75 households in the U.S. and an SRS of 80 households in the U.K. and calculate p̂₁ = the proportion of households in the U.S. sample that have a dog, and p̂₂ = the proportion of households in the U.K. sample that have a dog. Which of the following best describes the mean, variability, and shape of the sampling distribution of p̂₁ - p̂₂?

• Mean = 0.16, Standard deviation = 0.024, Shape = skewed to the right

• Mean unknown, Standard deviation unknown, Shape = approximately Normal.

• Mean = 0.16, Standard deviation = 0.024, Shape = approximately Normal.

• Mean unknown, Standard deviation unknown, Shape = skewed to the right

• Mean = 0.16, Standard deviation = 0.073, Shape = approximately Normal.

A study of 240 randomly selected residents of a subtropical resort city with 82,000 residents found that 5.4% of them had been exposed to the mosquito-borne virus that causes Dengue fever. Suppose the actual percentage of people in the city who have been exposed to the virus is 3%. Let p̂ = the proportion of residents who have been exposed in a random sample of 240. If the true proportion is actually 0.03, the probability that p̂ is more than 0.054 is closest to

• 0

• 0.0222

• 0.0207

• 0.0146

• We can’t calculate this probability because we have not satisfied the Normality condition.