AP Stats Review (Part 1)

In a certain region of the United States, the distribution of the number of siblings an individual has is strongly skewed to the right with a mean of 1.8 siblings. Which of the following is a possible value for the median of this distribution?

• 1

• 2

• 3

• 4

• 5

Answer explanation

The correct answer is (A). In a distribution that is skewed to the right, the value of the mean will be greater than the value of the median. Because the mean of this distribution is 1.8 siblings, the median must be less than 1.8 siblings. The only choice that is less than 1.8 is the value 1, so the median must be 1 sibling.

The phrase, household penetration, describes the percentage of households that purchase a particular item. The household penetration for toilet paper is 97%. You survey a random sample of 50 households and want to compute the probability that at least one of the households does not purchase toilet paper. Which of the following is appropriate for modeling this distribution?

• Binomial Distribution

• Geometric Distribution

• Normal Distribution

• t distribution

• Chi-square test

Answer explanation

The correct answer is (A). This situation is binary: success = buy toilet paper and failure = do not buy toilet paper, the trials are independent, there is a fixed number of trials (n = 50), and the probability of success remains the same for each trial (p = 0.97). Also note that because np = (50)(0.03) = 1.5, which is less than 10, a normal distribution is not an appropriate model.

An organization that strives to hold agencies accountable for truth in news reporting plans to select a random sample of 100 news stories from major U.S. news agencies in order to estimate the proportion of news stories produced by major U.S. news agencies that contain false information. A 90 percent confidence interval for the proportion of all news stories that contain false information will then be constructed.

Before selecting the sample, the organization determines that they want to make the margin of error as small as possible. Which of the following is the best way for them to decrease the margin of error? 

• Increase the confidence level to 95%.

• Increase the confidence level to 99%.

• Include a wider diversity of sources, such as local and international news agencies.

• Include news stories over a broad period of time, such as over the past decade.

• Increase the sample size.

Answer explanation

The correct answer is (E). With the confidence level and sample proportion held constant, the margin of error will decrease as the sample size increases. Also, note that when the confidence level is increased, the margin of error increases as well.

According to a report, more and more young adults are drinking coffee daily. An independent study conducted using a random sample of 500 young adults produces a 95 percent confidence interval for p, the proportion of all young adults who drink coffee daily. The interval was reported to be (0.14, 0.18). Which of the following interpretations is is correct?

• The margin of error for the given interval is 0.04.

• We can conclude that a majority of young adults drink coffee daily.

• There is a 95% probability that the true proportion of young adults that drink coffee is between 0.14 and 0.18.

• We can be 95% confident that the true proportion of young adults that drink coffee daily is between 0.14 and 0.18.

• If this procedure were to be repeated many times, 95% of the resulting confidence intervals will display that the true proportion of young adults that drink coffee daily is between 0.14 and 0.18.

Answer explanation

The correct answer is (D). Note that the margin of interval is 0.02 (half the length of the interval). The interval is not entirely above 0.5, so we cannot conclude that a majority of young adults drink coffee daily. The interval gives no information about what is happening over time. Finally, if we were to repeat the procedure many times, the resulting intervals would capture the true population proportion 95% of the time rather than strive to adhere to the results of this one random sample.

The supply manager at a local ice cream shop claims that 80% of customers prefer chocolate over vanilla. One of the employees believes that is an overstatement. He selects a random sample of 50 customers and found that 30 of them preferred chocolate over vanilla. Which of the following is the appropriate margin of error for a 95 percent confidence interval to estimate the population proportion of all customers that prefer chocolate over vanilla?

Answer explanation

The correct answer is (C). The critical value for a 95 percent confidence interval for one proportion is 1.96. The sample proportion  = 30/50 = 0.6 and the sample size n = 50. The value of 0.8 is not used in this case, because this is simply a claim that is made about the proportion of customers that prefer chocolate over vanilla. 

Professor Chauvet has 6 snake plants at her home. Two are small, two are medium, and two are large. She wants to see if the plants will grow taller if they are given water from her fish tank. She puts all the plants in her bay window at home so they receive equal amounts of sunlight. For the two small plants, she flips a coin to determine which one will get the water from the fish tank. She does the same for the medium, and large plants. She waters them this way weekly for 10 weeks.

After 10 weeks she compares the difference in growth for each set of 2 plants. Which of the following is the best description of the method she is using for data collection?

• An observational study

• A double-blind observational study

• An experiment with a completely randomized design

• An experiment with a randomized block design

• An experiment with a matched-pairs design

Answer explanation

The correct answer is (E). Professor Chauvet is conducting an experiment that uses a matched pairs design. She is comparing plant growth between very similar experimental units that are paired. The treatment (fish water or regular water) is randomly assigned within each pair.

Candidate A and Candidate B are running for president. You are planning a survey to determine what proportion of registered voters plan to vote for Candidate A p. You will contact a random sample of registered voters. You want to estimate p with 99% confidence and a margin of error no greater than 0.01. What is the minimum number of registered voters you will need to survey in order to meet these requirements?

• 97

• 166

• 6766

• 9604

• 16590

Answer explanation

The least-squares regression equation y^​=10+2x describes the relationship between x = age (in weeks) and y = weight (in pounds) for a sample of 50 German shepherd puppies for ages 5 ≤ x ≤ 20 weeks. The weight of a particular German Shepherd puppy that is 10 weeks old is underestimated by 10 pounds. How much does this particular puppy weigh?

• 10 pounds

• 20 pounds

• 30 pounds

• 40 pounds

• 50 pounds

Answer explanation

The correct answer is (D). A German Shepherd puppy that is 10 weeks old is predicted to weigh 10 + 2(10) = 30 pounds. Because the weight of this particular puppy is underestimated by 10 pounds, this puppy weighs 40 pounds.

The manager of a landscaping company collected data for an entire summer. Before each job he completely filled the gasoline tank for his mower. After each job, he recorded the square footage of the lawn that was mowed as well as how much gasoline remained in the tank. As expected, larger lawns left him with very little gasoline in the tank. At the end of the season he displayed the data in a scatterplot and saw that the relationship between lawn size and gas remaining was roughly linear.

The value of r^2 was 0.85. Find and interpret the value of the correlation between the lawn size and the amount of gasoline remaining in the tank at the end of the job.

• r=0.72. The linear relationship between lawn size and gas remaining is moderately strong and positive.

• r=0.92. The linear relationship between lawn size and gas remaining is strong and positive.

• r=−0.72. The linear relationship between lawn size and gas remaining is moderately strong and negative.

• r=−0.92. The linear relationship between lawn size and gas remaining is strong and negative.

• The value of the correlation cannot be determined without more information.

Answer explanation

Which of the following scenarios describes an experiment?

• A teacher plays classical music while her students take a test to determine if it will increase scores compared to the last test.

• A state cop uses a radar gun to measure the speed of the next 50 cars passing by.

• A firefighter records how many gallons of water are used to extinguish a fire each time they assist at a structure fire.

• A doctor asks his patients if they have any side effects with a certain medication and records their responses.

• A farmer notices that the crops that are planted on the east side of the property do not grow as well as those that are planted on the west side of the property.

Answer explanation

The correct answer is (A). Each of these choices describe an observational study except for the teacher. The teacher is imposing a treatment upon her students, so she is conducting an experiment.