Deck 7: Introduction to T Tests: Single Sample and Dependent Means

Question 1

Which of the following statements is true about t distributions?

A)There are exactly 10 categories of t distributions.
B)For any given sample size,there are between two and N - 1 appropriate t distributions.
C)The larger the sample size,the more a t distribution resembles a normal curve.
D)t distributions are generally bimodal.

Answer 1

The larger the sample size,the more a t distribution resembles a normal curve.

Question 2

If a sample includes 27 people,the degrees of freedom used in the formula to estimate the population variance would be

A)26
B)27
C)27²
D)√27

Answer 2

26

Question 3

A t test for dependent means would be used to compare

A)the level of honesty in politicians with the level of honesty in students.
B)the level of reading comprehension of students at the beginning and at the end of a speed-reading class.
C)the hours spent studying each week by freshmen and seniors.
D)the scores on a tolerance-of-diversity measure between two sororities.

Answer 3

the level of reading comprehension of students at the beginning and at the end of a speed-reading class.

Question 4

A school psychologist is using a depression inventory—on which a score of 0 indicates no depression and a score of 10 indicates severe depression—to see if the level of depression in fourth graders in a particular class of 20 students differs from that of fourth graders in general at a school. The results of previous testing indicate that fourth graders at the school usually have a score of 5 on the scale, but the variation is unknown. The current sample of 20 fifth graders has a mean depression score of 4.4.
If the psychologist figures S = .85,the effect size (d)is

A)5 / .85 = 5.88
B).85 / 5 = 0.17
C)(5 - 4.4)/ .85 = 0.71
D).85 / (5 - 4.4)= 1.42

Question 5

The main difference between a Z score and a t score is that

A)t scores are used when a study is analyzed with a one-tailed test.
B)t scores are used when the population variance is unknown.
C)t scores are used only when the sample size is greater than 30.
D)t scores are used only when inferences are made about other samples.

Question 6

The process of estimating the population variance from the scores in the sample involves

A)using a special table to find the estimated variance.
B)proceeding normally but interpreting the results with caution.
C)dividing the sum of squared deviations by N - 1 instead of N.
D)multiplying the sample variance by the degrees of freedom.

Question 7

A t test for a single sample would be used to compare

A)the level of honesty in politicians with the level of honesty in students.
B)the level of reading comprehension of students at the beginning and at the end of a speed-reading class.
C)the hours spent studying each week by freshmen and seniors.
D)the hours that "C" average students spend on Facebook each week compared with students in general.

Question 8

When conducting a t test for dependent means,μM

A)is always equal to 0.
B)is always equal to 1.
C)is always equal to -1.
D)depends on the population.

Question 9

In the formula for estimating the population variance from the sample,the sum of squared deviations is divided by

A)the number of participants in the sample.
B)the number of participants in the sample minus one.
C)the number of participants in the population.
D)the number of participants in the population minus one.

Question 10

If a sample includes three individuals with scores of 2,3,and 4,the estimated population variance is

A)1
B)1.33
C)2
D)3.67

Question 11

The difference between a t test for a single sample and a Z test for a single sample is the way

A)the problem is restated as a research hypothesis and a null hypothesis about the populations.
B)the mean of the known population is determined.
C)the variance of the known population is determined.
D)the decision about whether to reject the null hypothesis is made.

Question 12

A professor believes the students in a statistics class this term are more creative than most other students attending the university. A previous study found that students at the university had a mean score of 35 on a standard creativity test, and the current class has an average score of 40 on this scale with an estimated population standard deviation of 7. The standard deviation of the distribution of means is 1.63.
The t score is

A)(40 - 35)/ 7 = 0.71
B)(40 - 35)/ 1.63 = 3.07
C)(40 - 35)/ 7² = 5 / 49 = 0.10
D)(40 - 35)/ 1.63² = 5 / 2.66 = 1.88

Question 13

In a t test for dependent means,15 participants are each tested twice.This makes a total of 15 "before" scores and 15 "after" scores.What are the degrees of freedom?

A)15
B)14
C)30
D)29

Question 14

A school psychologist is using a depression inventory—on which a score of 0 indicates no depression and a score of 10 indicates severe depression—to see if the level of depression in fourth graders in a particular class of 20 students differs from that of fourth graders in general at a school. The results of previous testing indicate that fourth graders at the school usually have a score of 5 on the scale, but the variation is unknown. The current sample of 20 fifth graders has a mean depression score of 4.4.
The psychologist tests the null hypothesis that the level of depression of fourth graders in this class does not differ from fourth graders in general at the school and obtains a t score of -0.20.The decision regarding the null hypothesis would be to

A)reject it.
B)fail to reject it.
C)adjust the power.
D)increase the sample size.

Question 15

If a sample includes three individuals with scores of 4,6,and 8,the estimated population variance is

A)(2 + 0 + 2)/ 3 = 1.33
B)(2 + 0 + 2)/ 2 = 2
C)(4 + 0 + 4)/ 3 = 2.67
D)(4 + 0 + 4)/ 2 = 4

Question 16

A school psychologist is using a depression inventory—on which a score of 0 indicates no depression and a score of 10 indicates severe depression—to see if the level of depression in fourth graders in a particular class of 20 students differs from that of fourth graders in general at a school. The results of previous testing indicate that fourth graders at the school usually have a score of 5 on the scale, but the variation is unknown. The current sample of 20 fifth graders has a mean depression score of 4.4.
If the unbiased estimate of the population's variance is 15,the variance of the distribution of means is

A)15 / 20 = 0.75
B)15 / 19 = 0.79
C)15² / 20 = 11.25
D)15² / 19 = 11.84

Question 17

A professor believes the students in a statistics class this term are more creative than most other students attending the university. A previous study found that students at the university had a mean score of 35 on a standard creativity test, and the current class has an average score of 40 on this scale with an estimated population standard deviation of 7. The standard deviation of the distribution of means is 1.63.
If there were 30 students in the class and the professor wanted to test the null hypothesis described in the scenario using the 5% level of significance,the cutoff t score would be

A)35.000
B)1.699
C)-0.113
D)-2.500

Question 18

Which of the following statements about degrees of freedom is TRUE?

A)It always equals N - 2.
B)It is the number of scores in a sample that are free to vary.
C)It is used in effect size calculations.
D)It increases the bias inherent in a statistical estimate.

Question 19

A professor believes the students in a statistics class this term are more creative than most other students attending the university. A previous study found that students at the university had a mean score of 35 on a standard creativity test, and the current class has an average score of 40 on this scale with an estimated population standard deviation of 7. The standard deviation of the distribution of means is 1.63.
The effect size is

A)(40 - 35)/ 7 = 0.71
B)(40 - 35)/ 1.63 = 3.07
C)(40 - 35)/ 7² = 5 / 49 = 0.10
D)(40 - 35)/ 1.63² = 5 / 2.66 = 1.88

Question 20

When estimating the variance of a population from the sample,the sample variance cannot be used directly because

A)it is based on using absolute deviations.
B)it is based on using squared deviations.
C)it tends to be slightly too large-it overestimates the population variance.
D)it tends to be slightly too small-it underestimates the population variance.

Question 21

If an experimenter conducts a t test for dependent means with 10 participants and the estimated population variance of difference scores is 20,the variance of the comparison distribution is

A)20 / 10 = 2.0
B)20 / 9 = 2.2
C)400 / 10 = 40.0
D)400 / 9 = 44.4

Question 22

Your professor asks you to update a manuscript with the results of a t test for dependent means and provides you with the following information: there were 19 people in the study,the t score was 4.36,and the result was significant at the .01 level.The best way to present this information would be

A)t (19)= 4.36,p < .05
B)t (18)= 4.36,p < .01
C)t (4.36),p (.05)
D)t (4.36),p (.01)

Question 23

A medium effect size (d)for a t test for dependent means is

A).20
B).40
C).50
D).80

Question 24

The t test for dependent means is LEAST robust when

A)the population is highly skewed.
B)the population is normal.
C)there are more than 30 participants.
D)the population variance is small.

Question 25

If a t test for dependent means is reported in a research article as "t (16)= 2.67,p < .05," then

A)the result is not significant.
B)there were 16 participants.
C)the t score was 16.
D)the t score was 2.67.

Question 26

A counseling psychologist developing a technique to reduce procrastination has students time their procrastination for a week and uses this as a pretest measure of procrastination. Students then attend a workshop in which they are instructed to do a specific warm-up exercise for studying by focusing on a pleasant activity. Students again time their procrastination for a week, and the time from this second week is the posttest measure.
If the psychologist wants to see if there is a change (increase or decrease)in procrastination by 10 of the students who attended his workshop using the .05 significance level,the cutoff t score(s)would be

A)-.62,0,+2.62
B)+2.262
C)-2.262,0
D)-2.262,+2.262

Question 27

A counseling psychologist developing a technique to reduce procrastination has students time their procrastination for a week and uses this as a pretest measure of procrastination. Students then attend a workshop in which they are instructed to do a specific warm-up exercise for studying by focusing on a pleasant activity. Students again time their procrastination for a week, and the time from this second week is the posttest measure.
If the psychologist wants to see if there is a change (increase or decrease)in procrastination by students who attended his workshop,the appropriate description of "Population 2" (the comparison population)would be people whose

A)posttest scores will be lower than their pretest scores.
B)difference scores will be 0 or greater than 0.
C)difference scores will be 0.
D)difference scores will be smaller than their pretest scores.

Question 28

The most likely way for a t test to be presented in a research article for a study with 25 participants is

A)t (25)< significant
B)t (25)= 3.01,p < .05
C)t (24)= 2.94,p < .01
D)t (24)< significant

Question 29

Professor Q has designed a repeated measures experiment.Which information does he NOT need when looking up the power of his planned study in a power table?

A)whether a one- or two-tailed test will be computed
B)number of difference scores
C)estimated population variance of difference scores
D)effect size

Question 30

based on the following table from a research article.

Which of the following differences were significant at the .05 level?

A)Dominance
B)Independence
C)Conformity and Nurturance
D)All of the above

Question 31

based on the following table from a research article.

Which of the following statements is most likely to be true based on the results presented?

A)The hypothesis testing procedure probably used one-tailed tests.
B)The various scales probably all had just about the same population variances.
C)The t scores are all larger than the raw difference scores.
D)The hypothesis testing procedure was probably a t test for dependent means.

Question 32

Difference scores are computed for

A)a t test for a single sample.
B)a t test for dependent means.
C)a t test for independent means.
D)all t tests when the degrees of freedom are less than 10.

Question 33

"Student's" t test was invented by

A)Philip Guinness.
B)William Gosset.
C)Jacob Cohen.
D)Joan Guinness.

Question 34

A counseling psychologist developing a technique to reduce procrastination has students time their procrastination for a week and uses this as a pretest measure of procrastination. Students then attend a workshop in which they are instructed to do a specific warm-up exercise for studying by focusing on a pleasant activity. Students again time their procrastination for a week, and the time from this second week is the posttest measure.
If the psychologist finds that the sum of squared deviations from the mean of the difference scores of the sample is 135,the estimated population variance would be

A)135 / 10 = 13.5
B)135 / 9 = 15.0
C)10 / 135 = .074
D)9 / 135 = .067

Question 35

Studies using difference scores tend to have larger effect sizes than studies using other research designs because

A)of the long-standing procedural bias in psychology to set up studies involving dependent means in such a way as to artificially favor large effect sizes.
B)the standard deviation of difference scores is usually low.
C)participants provide their own baseline,which increases the variance.
D)studies with dependent means usually use a larger number of participants,so larger effect sizes are easily detected.

Question 36

based on the following table from a research article.

Which of the following differences were NOT significant?

A)Dominance
B)Independence
C)Conformity and Nurturance
D)None of the above-all were significant

Question 37

If a t test for dependent means is reported in a research article as "t (38)= 3.11,p < .01," then

A)the result is significant.
B)the result is not significant.
C)you can assume a one-tailed test was used.
D)there were 39 degrees of freedom.

Question 38

Which of the following is an assumption for the t test for dependent means?

A)The population variance is known.
B)The population mean is greater than the sample mean.
C)The population follows a normal distribution.
D)The sample follows a normal distribution.

Question 39

If 15 participants take a pretest and a posttest and have a mean difference score of 1.5,and if the standard deviation of the comparison distribution is 0.5,the t score is

A)0.5 / 1.5 = 0.33
B)1.5 / 15 = 0.10
C)1.5 / 0.5 = 3
D)1.5 / 0.5² = 6

Question 40

The comparison distribution in a t test for dependent means is a distribution of

A)means.
B)differences between means.
C)means of difference scores.
D)dependent means.

Question 41

If the mean of a sample is 95,the mean of Population 2 is 75,and the standard deviation of the distribution of means is 5,the t score resulting from a t test for a single sample is __________.(Give a number.)

Question 42

To find the score in a t table at which the null hypothesis will be rejected,an experimenter must know the significance level,the degrees of freedom,and __________.

Question 43

When figuring the variance of the distribution of means based on an estimated population variance in a study with 20 participants,you divide the estimated population variance by __________.(Give a number.)

Question 44

Given a particular number of degrees of freedom,there is(are)__________ t distribution(s).

Question 45

In the formula for effect size,d is for the difference between the means of the __________ divided by the variance.

Question 46

Before conducting a t test for dependent means on a set of pretest and posttest scores,the two sets of scores must be combined into one set of scores by figuring __________.

Question 47

Testing participants before and after an experimental manipulation is called a(n)__________ design.

Question 48

You are evaluating a non-directional hypothesis at the .01 significance level using a t test for a single sample.If there are 16 people in the sample,the cutoff score (critical value)needed is __________.

Question 49

In a t test for dependent means in which 10 participants are each tested twice,the number of degrees of freedom is __________.(Give a number.)

Question 50

When carrying out a t test for dependent means,a small effect size is __________.(Give a number.)

Question 51

The symbol S²_M represents the __________.

Question 52

When carrying out a t test for dependent means with a mean difference score of 12 and a standard deviation of the distribution of means of 6,the t score is __________.(Give a number.)

Question 53

The formula SS/df provides a(n)__________ estimate of the population variance.

Question 54

The formula (M - μ)/ S_M is used to figure the __________.

Question 55

In the formula (M - μ)/ S_M,S_M is the __________.(Describe in words.)

Question 56

The test used to reach a decision about the null hypothesis when the population variance is unknown is the __________ test.

Question 57

The more degrees of freedom,the closer a t distribution is to the __________.

Question 58

When figuring the variance of the distribution of means based on an estimated population variance,you divide the estimated population variance by __________.

Question 59

When carrying out a t test for dependent means with a mean difference score of 20 and a variance of the distribution of means of 25,the t score is __________.(Give a number.)

Question 60

The sum of squared deviations from the mean for a sample is 12,and there are 4 participants.The estimated population variance is __________.(Give a number.)

Question 61

When the results of a t test are presented in a research article,the number(s)in parentheses that directly follow the t score is(are)the __________.

Question 62

In terms of meeting assumptions of the t test for dependent means,the most common cause of serious problems is when a one-tailed test is used and the population distribution is highly __________.

Question 63

An organizational psychologist is hired as a consultant to a company planning to open a coffee house for college students.The company wants to know if their customers will drink more coffee if the coffee house is decorated in a Paris motif or in a San Francisco motif,so the psychologist sets up two similar rooms with the two motifs.Eight students spend an afternoon in each room,drinking all the coffee they like.The order in which they sit in the rooms is rotated so that half spend their first afternoon in the Paris room and half in the San Francisco room.The amount of coffee each participant drinks in each room is shown below.Using the .05 significance level,is there a significant difference between the numbers of cups of coffee consumed in the two rooms? a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size and find the approximate power of this study.
d.Explain the logic of what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample,including understanding decision errors,effect size and power,but who knows nothing about t tests of any kind (for example,you do not need to describe the steps or logic of hypothesis testing).Be sure you explain how this problem differs from a problem with a known population variance and a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and all the figuring you did to determine those characteristics.

Question 64

The results of a study using a t test for dependent means involving 45 participants that yielded a t score of 2.89,which was significant at the .01 level,would be reported in a journal article in symbols and numbers as __________.

Question 65

If the results of a study are reported in a research article as "t (29)= 2.31,p < .05," you can conclude that the result is __________.

Question 66

In a study to test the effects of science fiction movies on people's belief in the supernatural,seven people completed a measure of belief in the supernatural before and after watching a popular science fiction movie.Participants' scores are listed below with high scores indicating higher levels of belief.Using the .01 significance level,carry out a t test for dependent means to test the experimenter's assumption that the participants' belief in the supernatural would change after watching the movie. a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size and find the approximate power of this study.
d.Explain the logic of what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample,including understanding decision errors,effect size and power,but who knows nothing about t tests of any kind (for example,you do not need to describe the steps or logic of hypothesis testing).Be sure you explain how this problem differs from a problem with a known population variance and a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and all the figuring you did to determine those characteristics.

Question 67

t tests are often __________ to assumption violations.

Question 68

Knowing that a particular laboratory decision task takes the average person 2.5 seconds,an experimenter found that 30 randomly selected 80 year olds had a mean response time of 2.7 seconds with an estimated population standard deviation of 1.4 seconds.Using the .05 significance level,is the mean response time of older people slower than the response time of people in general?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Explain the logic of what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample,but who knows nothing about t tests of any kind (for example,you do not need to describe the steps or logic of hypothesis testing).Be sure you explain how this problem differs from a problem with a known population variance and a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and all the figuring you did to determine those characteristics.

Question 69

A social psychologist gave a questionnaire about concern for farm workers to seven participants before and after they attended a film about union organization of farm workers.The results are shown below with high scores meaning high concern.Using the .05 significance level,do these results support the hypothesis that the film affected concern for the lives of farm workers? a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size and find the approximate power of this study.
d.Explain the logic of what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample,including understanding decision errors,effect size and power,but who knows nothing about t tests of any kind (for example,you do not need to describe the steps or logic of hypothesis testing).Be sure you explain how this problem differs from a problem with a known population variance and a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and all the figuring you did to determine those characteristics.

Question 70

A swimming school claimed that the average seven-year-old would be able to swim across an Olympic-sized pool in less than 2 minutes after taking lessons from their instructors.To test this claim,a consumer psychologist arranged for eight randomly selected seven-year-old children to take lessons at the school and recorded how long it took each child to swim across a pool at the end of the lessons.The times (in seconds)were 60,120,110,80,70,90,100,and 130.What conclusion would the psychologist draw following a t test for a single sample using 120 seconds as the "known" population mean and the .05 significance level?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Explain the logic of what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample,but who knows nothing about t tests of any kind (for example,you do not need to describe the steps or logic of hypothesis testing).Be sure you explain how this problem differs from a problem with a known population variance and a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and all the figuring you did to determine those characteristics.

Question 71

An organizational psychologist wants to know if workers' health would improve if a company gave workers extra days off.All workers take a standard physical exam twice a year and are given an overall health rating with higher scores indicating better health.The psychologist selected five workers at random,arranged to have them receive an additional 2 days off every month over the period between health exams,and then compared the health scores on the two exams.Using the .05 significance level,do the scores in the table below support the notion that having extra days off improves health? a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size and find the approximate power of this study.
d.Explain the logic of what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample,including understanding decision errors,effect size and power,but who knows nothing about t tests of any kind (for example,you do not need to describe the steps or logic of hypothesis testing).Be sure you explain how this problem differs from a problem with a known population variance and a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and all the figuring you did to determine those characteristics.

Question 72

An industrial psychologist consulting with a chain of music stores knows that the average number of complaints management receives each month throughout the industry is 4,but the variance is unknown.Nine of the chain's stores were randomly selected to record complaints for one month; they received 2,4,3,5,0,2,5,1,and 5 complaints.Using the .05 significance level,is the number of complaints received by the chain different from the number of complaints received by music stores in general?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Explain the logic of what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample,but who knows nothing about t tests of any kind (for example,you do not need to describe the steps or logic of hypothesis testing).Be sure you explain how this problem differs from a problem with a known population variance and a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and all the figuring you did to determine those characteristics.