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1

Alpha Corporation developed a new pill to treat elevated glucose levels. They want to test the efficiency of the pill to lower glucose levels by gathering a sample of people with high glucose and giving them either:

  1. A daily dose of their new pill ("Experimental Group")

  2. A daily placebo pill that looks the same but does not do anything ("Placebo Group")

How can they make this a "Blind Study"?

Randomly sort people into the Experimental or Placebo groups, without letting them know which pill they received.

Give all participants both pills.

Give the pill to people with high blood glucose and low blood glucose.

Keep the participant identities hidden from the experimenters permanently.

Blindfold the participants while they take the pills.

Explanation

A blind experiment is one in which the participant does not know which experimental group they are in-- which is accomplished by not letting them know if they are in the Experimental or Placebo group.

2

Explanation

3

Which of the following is a discrete random variable?

The number of times heads comes up on 10 coin flips

The amount of water that passes through a dam in a random hour

The rate of return on a random stock investment

The length of a random caterpillar

Explanation

A discrete variable is a variable which can only take a countable number of values. For example, the number of times that a coin can come up heads in ten flips can only be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10. Thus, there are a countable number of possible outcomes (in this case 11). This is true for coin flips, but not for caterpillar length, water flow, or rates of return for stocks.

4

Find the Interquartile Range (IQR) for the following data.

Q1 = 2, Q3 = 6

IQR = Q3 - Q1 = 4

Explanation

The Interquartile Range equation is Q3-Q1

First, make sure the data is in ascending order. Then split the data up so that it each quartile has 25% of the data, or think of it as splitting the data into 4 equal parts.

  • is the "middle" value in the first half of the rank-ordered data set.
  • is the median value in the overall set.
  • is the "middle" value in the second half of the rank-ordered data set.

5

Alpha Corporation developed a new pill to treat elevated glucose levels. They want to test the efficiency of the pill to lower glucose levels by gathering a sample of people with high glucose and giving them either:

  1. A daily dose of their new pill ("Experimental Group")

  2. A daily placebo pill that looks the same but does not do anything ("Placebo Group")

How can they make this a "Blind Study"?

Randomly sort people into the Experimental or Placebo groups, without letting them know which pill they received.

Give all participants both pills.

Give the pill to people with high blood glucose and low blood glucose.

Keep the participant identities hidden from the experimenters permanently.

Blindfold the participants while they take the pills.

Explanation

A blind experiment is one in which the participant does not know which experimental group they are in-- which is accomplished by not letting them know if they are in the Experimental or Placebo group.

6

Your AP Statistics teacher asks you to conduct a survey to determine the most popular cereal brand at your high school. Which of the following should be the survey population in your study?

All students in your high school

Students in your AP Statistics Class

Students in your grade level

All high school students in your city

All high school students in the United States

Explanation

Since your teacher has asked that you determine the most popular cereal brand at your high school, the survey population should be limited to only your high school. Other students' preferences of cereal brands around the nation will have no impact on the survey results.

Additionally, surveying only students in your AP Statistics class or only students in a particular grade level would not be representative of all students in your high school. Therefore, the correct survey population is all students in your high school.

7

Alpha Corporation developed a new pill to treat elevated glucose levels. They want to test the efficiency of the pill to lower glucose levels by gathering a sample of people with high glucose and giving them either:

  1. A daily dose of their new pill ("Experimental Group")

  2. A daily placebo pill that looks the same but does not do anything ("Placebo Group")

How can they make this a "Blind Study"?

Randomly sort people into the Experimental or Placebo groups, without letting them know which pill they received.

Give all participants both pills.

Give the pill to people with high blood glucose and low blood glucose.

Keep the participant identities hidden from the experimenters permanently.

Blindfold the participants while they take the pills.

Explanation

A blind experiment is one in which the participant does not know which experimental group they are in-- which is accomplished by not letting them know if they are in the Experimental or Placebo group.

8

Which of the following is the best way to ensure a sample is representative and unbiased?

Take a random sample

Take a census

Take a voluntary response sample

Take a convenience sample

None of the other answers

Explanation

Taking a random sample is the only data-collecting method that ensures that every set of individuals has an equal chance of being selected for the sample and does not introduce any significant bias. Taking either a voluntary response sample or a convenience sample does not ensure these important aspects, as there is some unwanted selectivity involved in the data being collected. Taking a census is inferior to taking a sample of any sort, as it is both costly and time-consuming.

9

Which of the following is a discrete random variable?

The number of times heads comes up on 10 coin flips

The amount of water that passes through a dam in a random hour

The rate of return on a random stock investment

The length of a random caterpillar

Explanation

A discrete variable is a variable which can only take a countable number of values. For example, the number of times that a coin can come up heads in ten flips can only be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10. Thus, there are a countable number of possible outcomes (in this case 11). This is true for coin flips, but not for caterpillar length, water flow, or rates of return for stocks.

10

In a particular library, there is a sign in the elevator that indicates a limit of persons and a weight limit of . Assume an approximately normal distribution, that the average weight of students, faculty, and staff on campus is , and the standard deviation is .

If a random sample of people is taken, what is the standard deviation of their weights?

None of the other answers

Explanation

This question deals with the Central Limit Theorem, which states that a random sample taken from a large population where the sampling distribution of sample averages is approximately normal has a standard deviation equal to the standard deviation of the population divided by the square root of the sample size. The information given allows us to apply the Central Limit Theorem as it satisfies the necessary characteristics of the sampling distribution/size. The standard deviation of the population is 27lbs, and the sample size is 36; therefore, the standard deviation of the 36-person random sample is , which gives us 4.5lbs.

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