AP Statistics - 2013

Height, in meters, is measured for each person in a sample. After the data are collected, all the height measurements are converted from meters to centimeters by multiplying each measurement by 100. Which of the following statistics will remain the same for both units of measure?

• The mean of the height measurements

• The median of the height measurements

• The standard deviation of the height measurements

• The maximum of the height measurements

• The z-scores of the height measurements

A school principal wanted to investigate student opinion about the food served in the school cafeteria. The principal selected at random samples of 50 first-year students, 50 second-year students, 50 third-year students, and 50 fourth-year students to complete a questionnaire. Which of the following best describes the principal’s sampling plan?

• A stratified random sample

• A simple random sample

• A cluster sample

• A convenience sample

• A systematic sample

A candy company produces individually wrapped candies. The quality control manager for the company believes that the weight of the candies is approximately normally distributed with mean 720 milligrams (mg). If the manager’s belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights?

• 740 mg to 780 mg

• 700 mg to 740 mg

• 680 mg to 720 mg

• 660 mg to 700 mg

• 620 mg to 660 mg

A company currently uses Brand A lightbulbs, which have a mean life of 1,000 hours. A salesperson marketing Brand B, a new brand of bulb, contacts the company. The company will switch to the new brand of bulb only if there is convincing evidence that the mean life of Brand B is greater than 1,000 hours. Which of the following hypotheses should the company test?

• H₀: The mean life of Brand B is 1,000 hours.

  H₁: The mean life of Brand B is more than 1,000 hours

• H₀: The mean life of Brand B is 1,000 hours.

  H₁: The mean life of Brand B is less than 1,000 hours

• H₀: The mean life of Brand A is 1,000 hours.

  H₁: The mean life of Brand A is more than 1,000 hours

• H₀: The mean life of Brand A is 1,000 hours.

  H₁: The mean life of Brand A is less than 1,000 hours

• H₀: The mean life of Brand A is equal to the mean life of Brand B bulbs

  H₁: The mean life of Brand A is not equal to the mean life of Brand B bulbs

The amount of time required for each of 100 mice to navigate through a maze was recorded. The histogram below shows the distribution of times, in seconds, for the 100 mice. Which of the following values is closest to the standard deviation of the 100 times?

• 2.5 seconds

• 10 seconds

• 20 seconds

• 50 seconds

• 90 seconds

A graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph?

• The mean is greater than the median.

• The median is the average of the first quartile and the third quartile.

• There are fewer selling prices between the first quartile and the median than there are between the median and the third quartile.

• There are more selling prices that are less than the mean than selling prices that are greater than the mean.

• The value of maximum minus third quartile is less than the value of first quartile minus minimum.

A survey was conducted in which both men and women were asked a question about a current issue. Possible responses to this question were “in favor of,” “not in favor of,” or “no opinion.” A chi-square test is to be used to determine whether the response to this question is independent of gender. The number of degrees of freedom for the chi-square test in this situation is

• 6

• 5

• 3

• 2

• 1

If a probability distribution is symmetric, which of the following statements must be true?

• The distribution is normal.

• The distribution is uniform.

• The distribution is bimodal.

• The mean of the distribution is equal to the median of the distribution.

• The interquartile range of the distribution is equal to the standard deviation of the distribution.

Let X represent the number on the face that lands up when a fair six-sided number cube is tossed. The expected value of X is 3.5, and the standard deviation of X is approximately 1.708. Two fair six-sided number cubes will be tossed, and the numbers appearing on the faces that land up will be added. Which of the following values is closest to the standard deviation of the resulting sum?

• 1.708

• 1.848

• 2.415

• 3.416

• 5.835

Based on previous research, the standard deviation of the distribution of the age at which children begin to walk is estimated to be 1.5 months. A random sample of children will be selected, and the age at which each child begins to walk will be recorded. A 99 percent confidence interval for the average age at which children begin to walk will be constructed using the data obtained from the sample of children. Of the following, which is the smallest sample size that will result in a margin of error of 0.1 month or less for the confidence interval?

• 400

• 900

• 1,300

• 1,600

• 2,100