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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.
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**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

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