Deck 8: The Central Limit Theorem and Hypothesis Testing

Question 1

An "error" in statistics refers to a quality of the data that arises due to poor scientific skills.

Answer 1

False

Question 2

Descriptive statistics enable scientists to make predictions and estimate a phenomenon.

Answer 2

False

Question 3

Kinnebrook's error was that his recorded observations differed from someone else's observations.

Answer 3

True

Question 4

The Central Limit Theorem is not an assumption of inferential statistics as long as the sample size is large enough.

Question 5

The Central Limit Theorem allows scientists to make inferences about the population parameters based on an empirical set of observations.

Question 6

When researchers use parametric inferential statistics to make decisions, they are assuming that the Central Limit Theorem is true.

Question 7

Inferential statistics are used mainly for formality. If the sample mean of one group is larger than the other group, you can safely conclude that there was a statistically significant different based on the existence of a difference alone, without computing any statistics.

Question 8

The Central Limit Theorem makes claims about individual scores.

Question 9

The sampling distribution of means is a distribution of experimental effects.

Question 10

In a sampling distribution of means, the observations that make up a sample must be randomly selected.

Question 11

Under the Central Limit Theorem, the mean of your observed sample in an experiment will always be equal to the population mean.

Question 12

The further away from the distribution mean a sample mean is, the less likely it is to occur.

Question 13

The mean of a sampling distribution is the same value as the population mean.

Question 14

A sampling distribution that is made up of a sample size of 5 will have smaller variability than a sampling distribution that is made up of a sample size of 10.

Question 15

The standard deviation of a sampling distribution of n = 20 will be larger than the standard deviation of a sampling distribution of n = 50.

Question 16

A sample mean that falls within one standard deviation of the population mean is considered an outlier.

Question 17

In hypothesis testing, the null hypothesis is a hypothesis of an effect.

Question 18

If we know the actual means of our null and alternative populations, we do not need to conduct hypothesis testing.

Question 19

In hypothesis testing, you first have to select the alpha level before calculating the test statistic.

Question 20

Which of the following describes an "error" in statistics?

A) A careless mistake made by scientists during measurement of an observation.
B) A range of values obtained by measuring an observation.
C) The amount by which an observation differs from its expected value.
D) None of the above

Question 21

Which of the following was an important consequence of Kinnebrook's error?

A) His error showed that descriptive statistics can allow scientists to make judgements about a hypothesis.
B) His error actually led to him being right about his observations.
C) His error led to the discovery that differences between observers was the norm rather than the exception.
D) His error led to sailors getting lost at sea.

Question 22

Which of the following options describes the law of large numbers?

A) The mean of the results of an experiment repeated a large number of times will be close to the mean of the most recently conducted experiment.
B) The mean of the results of an experiment repeated a small number of times will be close to the mean of the results of an experiment repeated a large number of times.
C) The mean of the results of an experiment repeated a small number of times will be close to the mean of the experiment with the largest sample size.
D) The mean of the results of an experiment repeated a large number of times will be close to the mean of the population.

Question 23

Which of the following is true about the role of the Central Limit Theorem in statistics?

A) It allows scientists to reach a conclusion about the underlying population of what they are studying by using data from the actual population.
B) It allows scientists to reach a conclusion about the underlying population of what they are studying by using data from a sample.
C) It allows scientists to reach a conclusion about the observed sample that they are studying by using data from the actual population.
D) It allows scientists to reach a conclusion about the observed sample that they are studying by using data from the very same sample.

Question 24

Which of the following options reflect the Central Limit Theorem?

A) A large set of sample means will be normally distributed and the means of the samples that make up this large set will approximate the mean of the population.
B) A small set of sample means will be normally distributed and the means of the samples that make up this small set will approximate the mean of the population.
C) A small set of sampling errors will be normally distributed and the means of the samples that make up this small set will approximate the variability of the population.
D) A large set of sampling errors will be normally distributed and the means of the samples that make up this small set will approximate the variability of the population.

Question 25

In a sampling distribution of means…

A) There are all possible sizes of samples drawn from the population.
B) Samples are not always made up of randomly selected observations.
C) The mean tends away from the population mean.
D) The samples are all equal sizes.

Question 26

In a sampling distribution…

A) The x-axis displays the sample means and the y-axis displays the frequency.
B) The x-axis displays the frequency and the y-axis displays the sample means.
C) The x-axis displays the population means and the y-axis displays the frequency.
D) The x-axis displays the frequency and the y-axis displays the population means.

Question 27

Which of the following can we conclude if we assume that the Central Limit Theorem is true?

A) The mean of the observed sample will always equal the mean of the population.
B) The variability of the observed sample will always equal the variability of the population.
C) The mean of the sampling distribution of means will always equal the population mean.
D) The variability of the sampling distribution of means will always equal the variability of the population.

Question 28

The Central Limit Theorem is not made up of which of the following statements?

A) The distribution of sample means will approach a normal distribution as sample size increases.
B) The distribution of sample means will be more variable as sample size increases.
C) The mean of the distribution of sample means will always be equal to the mean of the population.
D) The standard deviation of the distribution of sample means will always be equal to the population standard deviation divided by the square root of the sample size.

Question 29

Which of the following is true about sampling distributions?

A) A distribution of sample means of n = 100 will have more variability than a distribution of sample means of n = 10.
B) A distribution of sample means of n = 100 will have a mean that is closer to the population mean than a distribution of sample means of n = 10.
C) A distribution of sample means of n = 100 will have a mean that is further away from the population mean than a distribution of sample means of n = 10.
D) A distribution of sample means of n = 100 will have less variability than a distribution of sample means of n = 10.

Question 30

Assuming that the Central Limit Theorem will apply, what is the probability that a randomly selected sample mean will be within one standard deviation of the population mean?

A) 33%
B) 50%
C) 68%
D) 95%

Question 31

The actual variability in the population is:

A) The same size as the variability in the sampling distribution of means.
B) Bigger than the variability in the sampling distribution of means.
C) Smaller than the variability in the sampling distribution of means.
D) Unrelated to the variability in the sampling distribution of means.

Question 32

To find standard error, you need:

A) Population mean and sample size
B) Population standard deviation only
C) Sample size only
D) Population standard deviation and sample size

Question 33

In the process of random sampling…

A) Each element of the population has an equal chance of being selected.
B) Each element of the eventual sample has an equal chance of being selected.
C) Selecting an element from the population will cause that particular element to have a much smaller chance of being selected again.
D) Selecting an element from the population is only truly random when sample size is large.

Question 34

Which of the following describes a "hypothesis"?

A) Form of truth derived from observation
B) Statement that is not true
C) Theoretical explanation
D) Type of empirical probability

Question 35

Which of the following is true about hypothesis testing?

A) The alternative hypothesis should always be non-directional.
B) The null and alternative hypotheses are theoretical predictions.
C) The null hypothesis should always be non-directional.
D) The null and alternative hypotheses are specified after selecting an alpha level.

Question 36

If Stacy hypothesizes that smelling her favorite perfume makes her happy, she is making:

A) A directional hypothesis
B) A non-directional hypothesis
C) A null hypothesis
D) An alternative null hypothesis

Question 37

If Stacy hypothesizes that going on a hike changes her stress levels, she is making:

A) A directional hypothesis
B) A non-directional hypothesis
C) A null hypothesis
D) An alternative null hypothesis

Question 38

Which of the following is true about the null and alternative hypotheses?

A) They are both non-directional.
B) They cannot co-exist in a single reality.
C) We can find the chances of each one being true by calculating the p-value.
D) None of the above.

Question 39

Which of the following is an example of the null hypothesis?

A) The mean of Group 1 will be the same as the mean of Group 2.
B) The mean of Group 1 will be larger than the mean of Group 2.
C) The mean of Group 1 will be smaller than the mean of Group 2.
D) The mean of Group 1 will increase with the mean of Group 2.

Question 40

Hypothesis testing is a process where…

A) No assumptions are made about the underlying distributions.
B) Data is collected, then analyzed, and finally an alternative hypothesis is formulated.
C) The probability of the null hypothesis being true is calculated.
D) None of the above.

Question 41

Which of the following expresses a non-directional hypothesis?

A) H₁: μ₀ ≠ μ₁
B) H₀: μ₀ ≠ μ₁
C) H₁: μ₀ < μ₁
D) H₀: μ₀ < μ₁

Question 42

David would like to examine whether keeping pets increases the wellbeing of children. He should formulate:

A) A directional hypothesis
B) A non-directional hypothesis
C) A null hypothesis
D) An alternative null hypothesis

Question 43

Show how you would obtain the standard error of a distribution of sample means given that the population mean is 10, the sample size is 50, the population variance is 4 and the sample mean is 30:

Question 44

A distribution of sample means has a standard error of 0.2 and a population standard deviation of 2. Find the sample size. Explain how you obtained your answer.

Question 45

List the statements that make up the Central Limit Theorem

Question 46

What is random sampling and why is it important in research?