AP Statistics 10.1 Warm Up

To investigate whether there is a difference in opinion on a certain proposal between two voting districts, A and B, two independent random samples were taken. From district A, 35 of the 50 voters selected were in favor of the proposal, and from district B, 36 of the 60 voters selected were in favor of the proposal. Which of the following is the test statistic for the appropriate test to investigate whether there is a difference in the proportion of voters who are in favor of the proposal between the two districts (district A minus district B)?

Answer explanation

There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious apples, 48 had blemishes. In a random sample of 75 of the red delicious apples, 42 had blemishes. Assume all conditions for inference have been met. Which of the following is closest to the interval estimate of the difference in the numbers of apples with blemishes (golden delicious minus red delicious) at a 98 percent level of confidence?

• (-0.076, 0.236)

• (-0.105, 0.265)

• (-10.5, 26.5)

• (-76, 236)

• (-105, 265)

Answer explanation

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.

Answer explanation

Researchers were investigating whether there is a significant difference between two medications, R and S, designed to reduce fleas found on cats. From a sample of 300 cat owners, the researchers randomly assigned 150 cat owners to use medication R on their cats and the remaining cat owners to use medication S. For the cats using medication R, 88 percent had no fleas. For the cats using medication S, 90 percent had no fleas. Which of the following is the most appropriate method for analyzing the results?

• A two-sample z-test for a difference in population proportions

• A two-sample z-test for a difference in sample proportions

• A one-sample z-test for a sample proportion

• A one-sample z-test for a population proportion

• A one-sample z-test for a difference in sample proportions

The mean and standard deviation of the sample data collected on continuous variable x are -0.25 and 0.03, respectively. The following table shows the relative frequencies of the data in the given intervals.

Based on the table, do the data support the use of a normal model to approximate population characteristics?

• Yes, because the sum of the relative frequencies is 1.00.

• Yes, because the distribution of relative frequencies is very close to the empirical rule for normal models.

• No, because the values are negative and normal models are used for positive values.

• No, because the distribution of relative frequencies is very far from the empirical rule for normal models.

• No, because the sample size and the population parameters are not known

Answer explanation