AP Stats Review Questions

Which of the following is the central limit theorem?

• No matter how the population is distributed, as the sample size increases, the mean of the sample means becomes closer to the mean of the population.

• No matter how the population is distributed, as the sample size increases, the standard deviation of the sample means becomes closer to the standard deviation of the population divided by the square root of the sample size.

• If the population is normally distributed, then as the sample size increases, the sampling distribution of the sample mean becomes closer to a normal distribution.

• None of these best describe the Central Limit Theorem.

If the correlation coefficient r=.78, what percentage of variation in y is explained by variation in x?

• 61%

• 44%

• 39%

• 78%

A telephone survey of 400 registered voters showed that 256 had not yet made up their minds 1 month before the election. How sure can we be that between 60% and 68% of the electorate were still undecided at that time?

• 2.4%

• 64.0%

• 90.5%

• 95.3%

What is a sampling distribution?

• A distribution of all the statistics that can be found in a given sample

• A histogram, or other such visual representation showing the distribution of a sample

• A normal distribution of some statistic

• A distribution of all the values taken by a statistic from all possible samples of a given size.

Assign each car in a dealership a number and then use a random-number table to select the cars to be inspected.

• systematic

• simple random sample

• convenience

• Self - selected (volunteer)

Interview every 10th student who enters the school in the morning.

• simple random

• voluntary response

• systematic

• convenience

An independent research company wants to go door to door to survey people in the city of Fontana. The company decides to number all blocks within the city limit, randomly choose 1 block and survey all households on that block.

This is an example of:

• Simple Random Sample

• Stratified Random Sample

• Cluster Random Sample

• Systematic Random Sampling

Have you ever run into someone you know when you were far away from home? A random sample of 1000 adults were asked this question. Here are their responses: Based on the responses, which of the following is a 90 percent confidence interval for the proportion of all adults who would respond that they have run into someone they know when they were far away from home?

• 0.801 ± 0.0325

Answer explanation

A manager of a local fast food restaurant wants to determine the average amount of time it takes from when a customer enters the drive-through line until they receive their order, regardless of the time of the day and the day of the week. That is, he would like to know the true average drive-through wait time for all his customers. Which of the following methods would be most likely to estimate the desired parameter with low bias and low variability?

• Select a random sample of 100 customers over a period of one month, determine each selected customer’s wait time, then compute the average wait time for all 100 customers.

• Select a random sample of 100 customers over a weekend, determine each selected customer’s wait time, then compute the average wait time for all 500 customers.

• Select a random sample of 500 customers on a randomly selected weekday, determine each selected customer’s wait time, then compute the average wait time for all 500 customers.

• Select a random sample of 500 customers over a weekend, determine each selected customer’s wait time, then compute the average wait time for all 500 customers.

• Select a random sample of 500 customers over a period of one month, determine each selected customer’s wait time, then compute the average wait time for all 500 customers.

Answer explanation

The correct answer is (E). In order to estimate the desired parameter with low bias, the manager should use a random sample over a long period of time. Limiting the data collection to just one weekend or one randomly selected weekday might introduce bias. Weekends may be busier than normal and may have longer wait times. Additionally, a larger sample size will produce an estimate that has lower variability than an estimate coming from a smaller sample size.

Which of the following distributions will best be modeled by a normal distribution?

• A bimodal distribution with a peak at 3, a peak at 10, and a standard deviation of 5.

• A uniform distribution with a mean of 5 for which 20% of the observations are between 1 and 3.

• A binomial distribution with n=150 and p=0.5.

• A geometric distribution with p=0.9

• A chi-square distribution with 2 degrees of freedom.

Answer explanation

The correct answer is (C). A binomial distribution with n = 150 and p = 0.5 can be modeled by a normal distribution because np = 150(0.5) = 75 ≥ 10 and n(1 – p) = 150(0.5) ≥ 10.