Statistics Unit 5 Review

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?

• Approximately normal with mean $206,274 and standard deviation $3,788

• Approximately normal with mean $206,274 and standard deviation $37,881

• Approximately normal with mean $206,274 and standard deviation $520

• Strongly right-skewed with mean $206,274 and standard deviation $3,788

• Strongly right-skewed with mean $206,274 and standard deviation $37,881

The director of a marketing department wants to estimate the proportion of people who purchase a certain product online. The director originally planned to obtain a random sample of 2,500 people who purchased the product. However, because of budget concerns, the sample size will be reduced to 1,500 people. Which of the following describes the effect of reducing the number of people in the sample?

• The variance of the sample will increase.

• The variance of the population will decrease.

• The variance of the sampling distribution of the estimator will increase.

• The variance of the sampling distribution of the estimator will decrease.

• The variance of the sampling distribution of the estimator will remain the same.

For the population of people in the United States who are at least 18 years of age, approximately 61 percent voted in a recent election. A random sample of 200 people and a random sample of 100 people will be selected from the population. For which sample size is it more likely that greater than 70 percent of the sample voted in the recent election?

• They are equally likely, because the mean of the sampling distribution is the same for both sample sizes.

• It is more likely for a sample size of 200 people, because there is more variability in the sampling distribution for larger sample sizes.

• It is more likely for a sample size of 200 people, because there is less variability in the sampling distribution for larger sample sizes.

• It is more likely for a sample size of 100 people, because there is more variability in the sampling distribution for smaller sample sizes.

• It is more likely for a sample size of 100 people, because there is less variability in the sampling distribution for smaller sample sizes.

The normal curve shown represents the sampling distribution of a sample mean for sample size n = 25, selected at random from a population with standard deviation σx̄. Which of the following is the best estimate of the standard deviation of the population, σx?

• 3

• 6

• 15

• 30

• 75

Samples G and H were selected from the same population of quantitative data and the mean of each sample was determined. The mean of sample G is equal to the mean of the population. Which of the following statements must be true? I. The mean of sample H must also be equal to the population mean. II. The mean of sample G, x̄G, is a point estimator for the mean of the population. III. The mean of sample H, x̄H, is a point estimator for the mean of the population.

• I only

• II only

• III only

• I and II

• II and III

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.

• Both R and W are biased.

• R is biased, and W is unbiased.

• R is unbiased, and W is biased.

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

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

• The centers will roughly be equal, and the variabilities will roughly be equal.

• The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

• The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

• The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

• The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (Note: z represents a standard normal random variable.)

• P(z > (0.27-0.22)/√((0.22)(0.78)/300))

• P(z > (0.27-0.22)/√((0.27)(0.73)/300))

• P(z > (0.27-0.22)/√((0.27)(0.78)/300))

• P(z > (0.22-0.27)/√((0.22)(0.78)/300))

• P(z > (0.22-0.27)/√((0.27)(0.73)/300))

A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteries is 400. A consumer group will obtain a random sample of 100 of the manufacturer’s batteries and will calculate the mean number of recharge cycles. Which of the following statements is justified by the central limit theorem?

• The sampling distribution of the sample mean will be approximately normal regardless of the shape of the population distribution.

• The sampling distribution of the sample mean will be exactly normal because the sample size is large.

• The sampling distribution of the sample mean will be approximately normal if the population distribution is normal.

• The sampling distribution of the sample mean will be approximately normal if the population distribution is skewed to the right.

• The sampling distribution of the sample mean will be approximately normal if the population distribution is skewed to the left.

The distribution of the number of recharge cycles for the sample is approximately normal because the population mean of 400 is greater than 30.

• True

• False