Deck 10: The T-Test

Question 1

The t-test allows you to make inferences from small samples with unknown population standard deviations.

Answer 1

True

Question 2

The standard deviation of a small sample is exactly the same as the standard deviation of the population.

Answer 2

False

Question 3

The t-distribution is perfectly normal regardless of the sample size.

Answer 3

False

Question 4

The formulae for calculating t- and z-tests share the exact same numerator.

Question 5

The denominator of the t-test is also known as the sample variance.

Question 6

The estimated standard error is a value that is obtained from the population.

Question 7

The denominator of the t-test is always a positive value.

Question 8

The numerator of the t-test is always a positive value.

Question 9

If the results of a t-test are statistically significant, then the t-statistic must be smaller than critical t.

Question 10

The degrees of freedom of a test must always be smaller than the sample size.

Question 11

In a one-sample t-test with a sample size of ten, the degrees of freedom of the test is nine.

Question 12

In a one-sample t-test, if the population mean is larger than the sample mean, the eventual t-statistic will be positive.

Question 13

T-tests in general require you to know more about the population than the z-test would require.

Question 14

An assumption of the independent samples t-test is that you have equal sample sizes in both groups that are being compared.

Question 15

An assumption of the independent samples t-test is that the two groups being compared must not be dependent on each other.

Question 16

If you are comparing two independent groups with very different variances, you should not use the independent samples t-test.

Question 17

The one-sample t-test has more assumptions than both the independent samples t-test and the dependent samples t-test.

Question 18

If researchers are not able to obtain twins for their experiments, then they are unable to use the dependent samples t-test.

Question 19

In a paired samples t-test, the variability of the two groups are not independent.

Question 20

The independent samples t-test is often chosen over the dependent samples t-test because it can account for individual differences.

Question 21

The Student's t-test…

A) Allows us to extend inferences made from a sample to the population.
B) Allows us to extend inferences made from a population to the sample.
C) Allows you to compare sample means if you know the population standard deviation.
D) Allows you to compare population means if you know the population standard deviation.

Question 22

Which of the following is not a type of t-test?

A) Single sample t-test
B) Dependent samples t-test
C) Independent samples t-test
D) Single score t-test

Question 23

Which of the following is true about both the t-test and the z-test?

A) The t and z distribution both depend on the observed sample.
B) The t and z-tests do not make any assumptions about the underlying population.
C) A p-value can be obtained by calculating the statistic of both tests.
D) None of the above.

Question 24

Which of the following terms is include in the numerator of the t-statistic formula?

A) Population mean
B) Standard error
C) Sample mean
D) Standard deviation

Question 25

The denominator of the t-test is the…

A) Estimated standard error
B) Population standard deviation
C) Estimated variance
D) Population variance

Question 26

Which of the following options correctly describes how to obtain the estimated standard error in a t-test?

A) Divide the population standard deviation by the sample size
B) Divide the population standard deviation by the square root of the sample size
C) Divide the sample standard deviation by the sample size
D) Divide the sample standard deviation by the square root of the sample size

Question 27

Which of the following statements correctly describes the symbol ?

A) It refers to the sample standard deviation and is a replacement of the population standard deviation that we do not know.
B) It refers to the sample variance and is a replacement of the population variance that we do not know.
C) It refers to the sample standard error and is a replacement of the population standard error that we do not know.
D) None of the above

Question 28

The degrees of freedom of a test…

A) Are unrelated to the sample size of the test.
B) Are unrelated to the outcome of the test.
C) Are unrelated to the p-value of the test.
D) None of the above.

Question 29

A one-sample t-test…

A) Allows you to make inferences about a sample when you do not know the population standard deviation and population mean.
B) Allows you to make inferences about a sample when you do not know the sample standard deviation.
C) Allows you to make inferences about a sample when you do not know the population standard deviation.
D) Allows you to make inferences about a sample when you do not know the population mean.

Question 30

If the t-statistic for a single sample t-test is 1.58, what can you conclude?

A) The test is significant at an alpha level of .05.
B) The sample size of the test was at least 30.
C) The sample mean was larger than the population mean.
D) The population standard deviation was smaller than the difference between the sample mean and the population mean.

Question 31

If a single sample t-test is statistically significant…

A) Then the sample mean must have been larger than the population mean.
B) Then the sample mean must have been smaller than the population mean.
C) Then the t-statistic must have fallen into the rejection region.
D) Then the t-statistic must not have fallen into the rejection region.

Question 32

In an independent samples t-test…

A) The population mean is known but the population standard deviation is unknown.
B) The population mean and population standard deviation are unknown.
C) The sample mean is known but the sample standard deviation is unknown.
D) The population mean and the sample standard deviation are unknown.

Question 33

In an independent samples t-test, which of the following options can take the place of the population mean?

A) Mean of the treatment group
B) Mean of the control group
C) Difference between the means of the treatment and control groups
D) None of the above

Question 34

Mike would like to find out if a new intervention would increase the motivation to study chemistry in high school students. He recruits 40 high schoolers and gives the intervention to 20 students. He then measures attitudes towards studying chemistry in all the students and compares the results for the students who got the intervention with the students who did not. Mike's study…

A) Has a non-directional hypothesis and should be tested with an independent samples t-test
B) Has a directional hypothesis and should be tested with an independent samples t-test
C) Has a non-directional hypothesis and should be tested with a dependent samples t-test
D) Has a directional hypothesis and should be tested with an independent samples t-test

Question 35

The denominator of the formula for an independent samples t-test is known as…

A) Estimated standard error
B) Population standard deviation
C) Estimated standard error of the difference
D) Estimated combined variability

Question 36

Which of the following is true about the sampling distribution of the difference between means?

A) It is used for one-sample t-tests and assumes that the central limit theorem is true.
B) It is used for one-sample t-tests and does not assume that the central limit theorem is true.
C) It is used for two-sample t-tests and assumes that the central limit theorem is true.
D) It is used for one-sample t-tests and does not assume that the central limit theorem is true.

Question 37

Which of the following correctly describes the phenomenon of subject mortality in relation to the independent samples t-test?

A) Subject mortality is a reason for the population mean falling in the rejection region of the distribution.
B) Subject mortality reduces the effect size and thus, should be avoided at all costs.
C) Subject mortality can cause sample sizes to be unequal for both groups being compared.
D) Subject mortality is mainly an ethical issue that has little effect on the actual t-test.

Question 38

Lucy would like to find out whether the amount of energy drinks consumed by her class is larger than the amount of energy drinks consumed by young adults on average. Which test listed below can be used to analyze her data?

A) One-sample t-test
B) Independent sample t-test
C) Repeated measures
D) None of the above

Question 39

Rachel is studying the effects of classical music exposure on math learning. She recruits 10 sets of twins and assigns one child in each pair to listen to classical music for an hour a day, and assigns the other child to listen to an audio book. At the end of a week, she gives each child a math lesson on tape and asks them to complete a math test. Rachel hypothesizes that classical music exposure will help math learning. What of the following is true about her study?

A) Rachel should use the independent samples t-test to account for potential subject mortality.
B) Rachel is able to eliminate the variance from individual differences due to her study design.
C) Since Rachel knows the population standard deviation, she should use the z-test.
D) Rachel is able to eliminate the variance from random chance due to her study design.

Question 40

Lianna would like to find out if a new type of therapy works. She recruits 15 patients with phobia and measures their phobia scores. Then, she gives them the therapy for 2 weeks. At the end of 2 weeks, she measures their phobia scores again. What test should Lianna use to examine her data?

A) Independent samples t-test
B) Dependent samples t-test
C) One-sample t-test
D) Z-test

Question 41

Moira has chosen to analyze her data with the dependent samples t-test. Which of the following options would make her choice invalid?

A) She has matched her subjects on dimensions relevant to the study.
B) She has taken care to randomly assign her subjects to one of two conditions.
C) She is using a repeated measures design.
D) None of the above.

Question 42

Lucinda has chosen to analyze her data with the independent samples t-test. Which of the following would make her choice invalid?

A) The variance of the two groups are not dependent on each other.
B) The two groups are about equal in variability.
C) Both groups being compared are of equal sizes.
D) None of the above.

Question 43

Which of the following correctly describes how to obtain the degrees of freedom for the independent samples t-test?

A) The degrees of freedom are equal to the sum of the sample sizes in both groups.
B) The degrees of freedom are equal to the average of the sample sizes in both groups.
C) The degrees of freedom are equal to the sum of the sample sizes in both groups, minus one.
D) The degrees of freedom are equal to the sum of the sample sizes in both groups, minus 2.

Question 44

Individual differences and random chance both contribute to…

A) Variability in the independent samples t-test
B) Variability in the dependent samples t-test
C) Population means in the independent samples t-test
D) Population means in the dependent samples t-test

Question 45

If Daisy obtains a t-statistic of -2.0 for a directional hypothesis with an alpha level of .05…

A) Daisy should reject the null hypothesis.
B) Daisy should fail to reject the null hypothesis.
C) Daisy should find the p-value so that she can decide whether to reject the null hypothesis.
D) There is insufficient information to decide if Daisy's decision is right.

Question 46

Find the estimated standard error if the variance of a sample is 16 and the sample size is 100. Show how you arrived at the answer.

Question 47

What information from raw data do you need to obtain the t-statistic of an independent samples t-test? Only list information that is needed. Listing irrelevant or redundant information will result in a deduction of points.

Question 48

Calculate the t-statistic for a one-sample t-test, given that the sample variance is 9, sample size is 64, sample mean is 35 and population mean is 36.

Question 49

What is the degrees of freedom of this test?

Question 50

Bill would like to find out if different study techniques lead to different grades. Describe a study design that Bill can carry out that will require him to analyze the data with an independent samples t-test. Describe a study design that Bill can carry out that will require him to analyze the data with a dependent samples t-test.

Question 51

Explain why, all things being equal, using the independent samples design and t-test is less likely to obtain a statistically significant effect than using the dependent samples design.