Deck 9: Tests for Significance: Paired and Independent-Samples T-Test

Question 1

Two observations linked together by a study's research design can be considered ______.

A) paired data
B) matched data
C) related data
D) all of these

Answer 1

D

Question 2

Which of the following is an example of paired data?

A) large and small organizations
B) high performing and low performing employees
C) male trainees and female trainees
D) none of these

Answer 2

D

Question 3

Which of the following is an example of repeated measures data?

A) male trainees and female trainees
B) quick learners and slow learners
C) learning before and after training
D) none of these

Answer 3

C

Question 4

Which of the following is an example of repeated measures data?

A) sales figures this year and last year
B) yearly performance evaluations over the past three years
C) employee turnover for the past five years
D) all of these

Question 5

Which of the following is an example of paired data?

A) two employees
B) an employee and their immediate supervisor
C) two supervisors
D) all of these

Question 6

Of the following, the calculations for the paired samples t-test are most similar to ______.

A) independent samples t-test
B) one-sample t-test
C) z-test
D) confidence interval

Question 7

The parameter of interest in a paired samples t-test is ______.

A) µ
B) µ_D
C) µ₁ - µ₂
D) none of these

Question 8

Which of the following is most likely what µ_D represents?

A) µ_time2 - µ_time1
B) µ_time2 + µ_time1
C) µ_time2 * µ_time1
D) none of these

Question 9

The sample estimate of µ_D is ______.

A) s_D
B) x?
C) x? _D
D) ${ }^{s_{D_{\bar{x}}}}$

Question 10

The standard error of the mean difference is represented with ______.

A) s_D
B) x?
C) x? _D
D) ${ }^{s_{D_{\bar{x}}}}$

Question 11

If your dataset contains twenty pairs of data, the degrees of freedom for your paired samples t-test will be ______.

A) 20
B) 19
C) 39
D) 38

Question 12

You collect a sample of ten pairs of pre- and post-training test scores. If _D = 1.1 and s_D = 1.37, what is the observed value of t?

A) 2.539
B) 1.833
C) .80
D) none of these

Question 13

You collect a sample of twenty pairs of yearly sales in 2000 and 2005. You hypothesize that yearly sales have decreased between 2000 and 2005. If _D = -99.6 and s_D = 160.60, what is the critical value of t if $\alpha$ = .05?

A) -1.729
B) -2.093
C) 1.725
D) 1.086

Question 14

You collect a sample of thirty pairs of production counts per hour. You hypothesize that production counts per hour have increased between Time 1 and Time 2. If _D = 19.1 and s_D = 16.058836, what is the appropriate conclusion if $\alpha$ = .05?

A) retain the null
B) reject the alternative
C) reject the null
D) none of these

Question 15

You collect a sample of twenty pairs of production counts per hour. You hypothesize that production counts per hour have increased between Time 1 and Time 2. If _D = 15.15 and s_D = 14.357375, what is the standardized effect size?

A) 15.15
B) 4.72
C) 1.06
D) 3.21

Question 16

Which of the following is an example of data appropriate for an independent samples test?

A) large and small organizations
B) high performing and low performing employees
C) male trainees and female trainees
D) all of these

Question 17

Which of the following is an example of appropriate for an independent samples test?

A) employees from Branch A and employees from Branch B
B) employees pre- and post-training
C) sales in 2000 and sales in 2008
D) all of these

Question 18

The parameter of interest in an independent samples t-test is ______.

A) µ
B) µ_D
C) µ₁ - µ₂
D) none of these

Question 19

Which of the following is most likely what µ₁ - µ₂ represents?

A) the hypothesized mean difference in the population
B) the hypothesized mean difference in the sample
C) the standard error
D) none of these

Question 20

We must calculate the pooled variance because ______.

A) we need to compute a standard error for each sample
B) we need to compute a single standard error for two samples
C) we do not have information about the variance of each sample
D) all of these

Question 21

If your dataset contains twenty scores, the degrees of freedom for your independent samples t-test will be ______.

A) 20
B) 19
C) 18
D) 38

Question 22

You collect a sample of 8 performance evaluation scores from Company A and 8 performance evaluation scores from Company B. Ifx̄ ₁ =5 x̄₂= 3 and s_p² = 1.25, what is the observed value of t?

A) 3.58
B) 1.60
C) 1.79
D) 5.06

Question 23

You collect a sample of 15 survey scores from customers of Company A and 15 survey scores from customers of Company B. If ₁ =3.1 ₂= 1.9 and s_p² = 2.55, what is the critical value of t for a two-tailed test if $\alpha$ = .05?

A) ± 2.045
B) ± 2.048
C) ± 1.701
D) ± 1.699

Question 24

You collect a sample of 20 monthly employee salaries from Branch A and 20 monthly employee salaries from Branch B. If ₁ = 5100.8 , ₂ = 3837.7, s₁ = 945.199316 and s₂ = 912.399099, what is the value of the pooled variance?

A) 928.94
B) 293.76
C) 862936.93
D) none of these

Question 25

You collect a sample of 10 monthly production counts from Company A and 10 monthly production counts from Company B. You hypothesize that production counts for Company B will be greater than production counts from Company A. If x̄₁ = 46 , x̄₂ = 52.3 s_p² = 76.338889, what is the appropriate conclusion if $\alpha$ = .05?

A) retain the null
B) accept the alternative
C) reject the null
D) none of these

Question 26

You collect information about the number of employees that arrive to work late. Employees are categorized in two groups: those hired more than 6 months ago (Group 1) and those hired less than 6 months ago (Group 2). You hypothesize that employees that were hired more than 6 months ago will have lower mean days late than those hired less than six months ago. If x̄₁ = 1.8, x̄₂ = 3.5, s₁ = 0.78811 and s₂ = 0.707107, what is the appropriate conclusion if $\alpha$ = .05?

A) retain the null
B) reject the alternative
C) reject the null none of these

Question 27

You collect satisfaction data from 5 clients of Company A and 5 clients of Company B. If x̄₁ = 65.6 , x̄₂ = 42.8, s_p² = 106.25, what is the standardized effect size?

A) 22.8
B) 2.21
C) 3.5
D) none of these

Question 28

The order of mean subtraction for the independent samples t-test is dependent on ______.

A) the phrasing of the research question
B) the direction of the critical value
C) the sign used in the hypotheses
D) all of these

Question 29

The paired samples t-test and the independent samples t-test are similar in that they both ______.

A) examine t by dividing a mean difference by a standard error
B) require an estimate of the standard error
C) compare two conditions
D) all of these

Question 30

The samples in paired samples t-tests are ______ whereas the samples in independent samples t-tests are ______ .

A) related, related
B) related, unrelated
C) unrelated, related
D) unrelated, unrelated

Question 31

Repeated measures data always has exactly two time points

Question 32

All paired data are repeated measures data

Question 33

All repeated measures data are also paired data

Question 34

When conducting a paired samples test on Time 1 and Time 2 data, it is clearest to subtract Time 2 from Time 1.

Question 35

When asking if there is a difference in a paired samples test, the value of µ_D is always 0.

Question 36

µ_D is the mean of a population

Question 37

Paired samples, matched samples, and related samples t-tests are all the same.

Question 38

In a paired samples t-test when n = 10, must contain at least 20 data.

Question 39

In a two-tailed paired sample test, when n = 51, t_crit = ±2.009

Question 40

is the standard error used in a paired samples t-test.

Question 41

The only difference in the formula for the sample standard error of the difference and the sample standard error of the mean is the use of s_D instead of s.

Question 42

If t(25) = 2.9, we should reject the null.

Question 43

When calculating paired samples t-test, we should always compute a confidence interval.

Question 44

Independent samples come from independent sources.

Question 45

A variable where 0 and 1 are used to indicate group membership is a called an affiliation variable.

Question 46

The subtraction order in an independent samples t-test is not important.

Question 47

Unlike a paired samples t-test, an independent samples t-test examines 2 µ's simultaneously.

Question 48

When we reject the null in an independent samples t-test, we conclude that our 2 samples are likely to come from the same population.

Question 49

Degrees of freedom for an independent samples t-test is n-1.

Question 50

In an independent samples t-test, we assume that the variances in our populations are the same.

Question 51

Given a particular dataset, how would you determine if a paired samples or an independent samples t-test were appropriate?

Question 52

Conceptually, how are the formulas for the independent samples t-test and the paired samples t-test similar? How are they different?

Question 53

Define and describe

Question 54

For an independent samples t-test, describes how you know which direction to subtract the group means.

Question 55

In the dataset above, sales numbers are recorded for each of our 10 employees both today and one year ago. Last year, we implemented a new training program and we would like to see if this has increased sales.
1) State the research question.
2) State the hypotheses.
3) State the critical value.
4) Provide the formal test of the hypothesis.
5) State the confidence interval.
6) Is an effect size calculation appropriate? How do you know? If yes, calculate both a standardized and unstandardized effect size.
7) State all appropriate conclusions.

Question 56

You're interested in differences in Revenue due to customer service orientation. Specifically, you want to know if organizations that are not customer service oriented have lower mean Revenues than organizations that are customer service oriented.
1) State the research question.
2) State the hypotheses.
3) State the critical value.
4) Provide the formal test of the hypothesis.
5) Is an effect size calculation appropriate? How do you know? If yes, calculate both a standardized and unstandardized effect size.
6) State all appropriate conclusions.