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AP Stats

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Unit 5

5.10 MC Answers and Review

6 min read•december 10, 2021

AP Statistics 📊

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Answers and Review for Multiple Choice Practice on Sampling Distributions

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⛔STOP ⛔ Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in Unit 5. Click here for the practice questions: AP Statistics Unit 5 Multiple Choice Questions.

Facts about the test: The AP Statistics exam has 40 multiple choice questions and you will be given 1 hour 30 minutes to complete the section. That means it should take you around 11 minutes to complete 5 questions.

The following questions were not written by College Board and although they cover information outlined in the AP Statistics Course and Exam Description the formatting on the exam may be different.

1. Which of the following describes a sampling distribution?

A. A sampling distribution is a distribution of all parameter values from a given sample.

B. A sampling distribution is a distribution of all values from a given population.

C. A sampling distribution is a distribution of all values of a sample from a given population.

D. A sampling distribution is the distribution of values of a statistics for all possible samples of a given size from the same population.

Answer: The main thing about a sampling distribution that is necessary to know is that it is the distribution from all possible samples of a given size. Normally we use one sample to estimate what our sampling distribution may look like.

📄 Study AP Statistics, Unit 5.0: Unit 5 Overview

2. What is the area under any given density curve, namely the normal distribution?

A. 0.5

B. 30

C. 0.1

D. 1

Answer: The area under any density curve is 1. This is extremely helpful when using the normal distribution because we know that it captures all possible outcomes of a given event, therefore, the area between two bounds can give us the probability of certain events happening.

📄 Study AP Statistics, Unit 5.2: The Normal Distribution, Revisited

3. The central limit theorem states that for our sampling distribution for a population ________ to be approximately normal, the sample size must be _________.

A. mean, 10

B. mean, 30

C. proportion, 10

D. proportion, 30

Answer: The central limit theorem applies to means and uses 30 as the bound in which a sampling distribution is approximately normal. n>=30.

📄 Study AP Statistics, Unit 5.3: The Central Limit Theorem

4. If our sample statistic is ________________, it is a good estimator of our population parameter.

A. Biased

B. Variable

C. Unbiased

D. Quantitative

Answer: Bias refers to how good our sampling distribution estimates the population. A good sampling distribution would be centered around the population parameter.

📄 Study AP Statistics, Unit 5.4: Biased and Unbiased Point Estimates

5. The mean of a sampling distribution for a population proportion is _______.

A. p

B. μ

C. σ

D. np

Answer: If we are looking for the center, or mean of our sampling distribution for proportions, we must use our population proportion, p.

📄 Study AP Statistics, Unit 5.1: Introducing Statistics: Why Is My Sample Not Like Yours?

6. What requirement of our sample gives us evidence that the sampling distribution would be unbiased?

A. Low variability

B. Highly biased sample

C. Sample done with blocking

D. Randomly selected sample

Answer: A random sample is necessary to show us that our sample statistic is unbiased.

📄 Study AP Statistics, Unit 5.4: Biased and Unbiased Point Estimates

7. Which of the following gives the standard deviation of a sampling distribution for means?

A. σ/sqrt(n)

B. σ/n

C. σ*n

D. 2nσ

Answer: The standard deviation of a sampling distribution for means can be found by dividing the given standard deviation by the square root of n. This formula is located on your formula sheet.

📄 Study AP Statistics, Unit 5.5: Sampling Distributions for Sample Proportions

8. The large counts condition is used to show that the sampling distribution for a population __________ is normal by stating that the number of successes and failures is at least _____.

A. mean, 10

B. mean, 30

C. proportion, 10

D. proportion, 30

Answer: The large counts condition is used with proportions and states that the number of successes and failures in our sample is at least 10. np>=10 and n(1-p)>=10.

📄 Study AP Statistics, Unit 5.5: Sampling Distributions for Sample Proportions

9. A researcher takes a random sample of 80 students from a large local high school to determine their average number of days absent from school. In order to use the standard deviation formula, our school population size must be at least _______.

A. 30

B. 800

C. 1800

D. 10

Answer: The 10% condition states that our population must be 10 times our sample size in order to use the standard deviation formula for a sampling distribution. This minimizes the effects of drawing our sample without replacement.

📄 Study AP Statistics, Unit 5.0: Unit 5 Overview

10. When describing a sampling distribution, which of the following isn't necessary?

A. Shape/Approximately Normal

B. Unusual Features

C. Context

D. Spread

Answer: It isn't necessary to describe unusual features of a sampling distribution IF your sampling distribution is approximately normal (which it normally is). Being normal means that it would not have outliers or any gaps.

📄 Study AP Statistics, Unit 5.5: Sampling Distributions for Sample Proportions

11. What symbol is used for a population mean?

A. ρ

B. σ

C. μ

D. x-bar

Answer: The greek letter mu is used for the population mean, while x-bar is used for sample mean.

📄 Study AP Statistics, Unit 5.1: Introducing Statistics: Why Is My Sample Not Like Yours?

12. Which of the following would have the smallest standard deviation

A. Sample size of 100

B. Sample size of 10

C. Sample size of 1

D. Sample size of 5

Answer: When sample size increases, standard deviation decreases. Therefore, the largest sample size would have the smallest standard deviation.

📄 Study AP Statistics, Unit 5.5: Sampling Distributions for Sample Proportions

13. A study group is looking to determine what proportion of US adults aged 75+ work out on a regular basis. To do so, they take a sample of 80 US adults aged 75+. Identify the population.

A. All US adults

B. 80 US adults aged 75+

C. All US adults aged 75+

D. All US citizens

Answer: Since our sample is only adults in the US aged 75+, our population is limited to US adults aged 75+.

14. A population distribution is strongly skewed right with 3 outliers. What would the sampling distribution look like with a sample size of 100?

A. Slightly skewed right

B. Strongly skewed right

C. Skewed left

D. Approximately normal

Answer: Since our sample size is considerably large, our sampling distribution will be approximately normal regardless of the population distribution shape.

📄 Study AP Statistics, Unit 5.2: The Normal Distribution, Revisited

15. The average of all students on the ACT scores a 19 with a standard deviation of 1.5. What is the probability of randomly selecting a sample of 100 students where the average score is 30 or above?

A. 0.2

B. 0.4

C. 0

D. 0.1

Answer: The probability of selecting a random sample of 100 students where their score is 30+ is essentially 0. While it is technically possible, it is extremely unlikely. Three standard deviations away from our population mean is 23.5 (sample size of 1). When we factor in a sample size of 100, our standard deviation would be considerably smaller (0.15), so it is practically impossible to find a sample that is 73.33 standard deviations away from the mean.

📄 Study AP Statistics, Unit 5.2: The Normal Distribution, Revisited

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