Deck 8: Introduction to the T Test: Single Sample and Dependent Means

Question 1

If you know the sample's variance but not the population's variance:

A)you can look up the population's variance on a table
B)you can do a t test anyway, because variance is unrelated to the process
C)you should avoid making inferences based on your data
D)you can estimate the population's variance from the scores in the sample

Answer 1

you can estimate the population's variance from the scores in the sample

Question 2

The variance of a sample is said to be "biased" because it consistently __________ the actual variance of the population.

A)overestimates
B)underestimates
C)enlarges
D)divides

Answer 2

underestimates

Question 3

A local newspaper reports that young women in your town (i.e., a known population)sleep an average of only 5 hours per night. However, you think that women in your town who are enrolled at your college sleep more than that. You randomly select 200 women from your college and ask them to accurately record their hours of sleep. You find that they sleep an average of 7 hours per night. What test would you use to determine whether this mean difference is statistically meaningful?

A)ANOVA
B)t test for dependent means
C)t test for a single sample
D)regression

Answer 3

t test for a single sample

Question 4

Gosset discovered the t distribution while attempting to:

A)improve the quality of life for German students
B)improve the quality of beer for Guinness brewers
C)solve the mystery of the normal curve
D)conduct experiments related to genes and environment

Question 5

Which of the following 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.

Question 6

The number of scores free to vary when estimating a population parameter is/are:

A)degrees of freedom
B)number of scores minus 1
C)number of scores multiplied by the standard deviation
D)both A and B

Question 7

When estimating the population's variance from the scores in a sample, you should:

A)look on a special table to find the estimated variance
B)proceed normally, but interpret the results with caution
C)divide the sum of squared deviations by N-1 instead of N
D)multiply the sample's variance by the degrees of freedom

Question 8

The t test is sometimes called __________ because its main principles were developed by William Gosset who published his articles anonymously using the name "__________."

A)Student's t; Student
B)Standard's t; Standard
C)Gosset's t; Gosset
D)Standard's t; Gosset

Question 9

A sample has individuals with scores of 1, 3, 5, 6, and 6. What is the estimated population variance?

A)3)6
B)4)7
C)5)8
D)6)9

Question 10

If a sample has 45 people in it, the degrees of freedom used in the formula to estimate the population variance would be:

A)45²
B)45/2
C)44
D) .22

Question 11

In the formula for estimating the population variance from the scores in a 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 12

Suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. She figures her t score to be -.20. What decision should she make regarding the null hypothesis?

A)Reject it
B)Fail to reject it
C)Postpone any decisions until a more conclusive study could be conducted
D)There is not enough information given to make a decision

Question 13

All of the following statements are true about t tests EXCEPT:

A)they involve hypothesis-testing procedures
B)they are used when the population variance is unknown
C)they are used when the population variance is known
D)they compare t scores from a sample to a comparison distribution called a t distribution

Question 14

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

A)26
B)27
C)27²
D)square root of 27

Question 15

A sample has three individuals, with scores of 2, 3, and 4. What is the estimated population variance?

A)1
B)1)33
C)2
D)3)67

Question 16

When estimating the variance of a population from the sample, you cannot use the sample's variance 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
D)it tends to be slightly too small

Question 17

The __________ is a hypothesis-testing procedure used when a sample mean is being compared to a known population mean and the population variance is unknown.

A)ANOVA
B)t test for a single sample
C)t test for multiple samples
D)Z test

Question 18

For the following question(s): A school counselor tests the level of depression in fourth graders in a particular class of 20 students. The counselor wants to know whether the kind of students in this class differs from that of fourth graders in general at her school. On the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. From reports, she is able to find out about past testing. Fourth graders at her school usually score 5 on the scale, but the variation is not known. Her sample of 20 fifth graders has a mean depression score of 4.4. Use the .01 level of significance.
The counselor calculates the unbiased estimate of the population's variance to be 15. What is the variance of the distribution of means?

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

Question 19

Which of the following is TRUE?

A)An example of an unbiased estimate is the variance of a sample; a typical biased estimate is the researcher's initial expectation prior to sampling.
B)There is only one biased estimate (i.e., the researcher's expected findings); there are several unbiased estimates.
C)A biased estimate is preferred to an unbiased estimate when the population is not normally distributed.
D)A sample's variance is a biased estimate of the population's variance, but a slight change in the variance formula gives an unbiased estimate.

Question 20

What is the main difference between Z score and t score?

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

Question 21

Another name for difference scores is:

A)change scores
B)dependent scores
C)scores
D)deleted scores

Question 22

For the following question(s): Professor Juarez thinks the students in her statistics class this term are more creative than most students at this university. A previous study found that students at this university had a mean score of 35 on a standard creativity test. Professor Juarez finds that her class scores an average of 40 on this scale, with an estimated population standard deviation of 7. The standard deviation of the distribution of means comes out to 1.63.

-What effect size did Professor Juarez find?

A)(40 - 35)/7 = .71
B)(40 - 35)/1.63 = 3.07
C)(40 - 35)/7² = 5/49 = .10
D)(40 - 35)/1.63² = 5/2.66 = 1.88

Question 23

A research strategy in which each person is tested more than once is known as:

A)within-subjects design
B)repeated-measures design
C)before-after design
D)any of the above

Question 24

The shape of a t distribution:

A)is typically bimodal
B)is typically rectangular
C)will vary according to the mean of the population you used to estimate sample variance
D)will vary according to the degrees of freedom in the sample you used to estimate population variance

Question 25

The t score is your sample's mean minus the __________ divided by the __________.

A)sample size; variance of the distribution of means
B)sample size minus 1; standard deviation of the distribution of means
C)population mean; standard deviation of the distribution of means
D)population median; variance of the distribution of means

Question 26

You do a t test for dependent means in exactly the same way as a t test for a single sample, except that you use something called:

A)the mean variance
B)variance of the dependent means
C)difference scores
D)independent t scores

Question 27

Difference scores are usually used with:

A)a t test for a single sample
B)a t test for dependent means
C)a t test for independent means
D)all of the above

Question 28

For the following question(s): Professor Juarez thinks the students in her statistics class this term are more creative than most students at this university. A previous study found that students at this university had a mean score of 35 on a standard creativity test. Professor Juarez finds that her class scores an average of 40 on this scale, with an estimated population standard deviation of 7. The standard deviation of the distribution of means comes out to 1.63.

-What is the t score?

A)(40 - 35)/7 = .71
B)(40 - 35)/1.63 = 3.07
C)(40 -35)/7² = 5/49 = .10
D)(40 - 35)/1.63² = 5/2.66 = 1.88

Question 29

In a study with 15 degrees of freedom, what would be your cutoff score for a t distribution using a two-tailed test at the .01 level of significance?

A)2)603
B)1)753
C)2)132
D)2)947

Question 30

If Professor Juarez had 30 students in her class, and she wanted to test her hypothesis using the 5% level of significance, what cutoff t score would she use? (You should be able to figure this out without a table because only one answer is in the correct region.)

A)304.11
B)1.699
C)-.113
D)-2.500

Question 31

The difference between a person's score on one testing and the same person's score on another testing:

A)test score
B)deleted score
C)distance score
D)difference score

Question 32

Other names for the t test for dependent means include all of the following EXCEPT:

A)paired-sample t test
B)t test for matched samples
C)t test for matched pairs
D)independent-sample t test

Question 33

Suppose the standard deviation she figures (the square root of the unbiased estimate of the population variance)is .85. What is the effect size?

A)5/.85 = 5.88
B) .85/5 = .17
C)(5 - 4.4)/.85 = .71
D) .85/(5 -4.4)= 1.42

Question 34

In which situation below would you use a t test for dependent means?

A)To compare the level of honesty (based on an honesty scale)in politicians to the level of honesty in students.
B)To compare the level of reading comprehension of students at the beginning of a speed-reading class to their level of reading comprehension at the end of the class.
C)To find the correlation between liking for coffee and tendency to be a "night person" among a group of students.
D)To compare the scores on a tolerance-of-diversity measure between two sororities.

Question 35

In what important way does a t distribution differ from a normal curve?

A)it has slightly less scores at the extremes
B)it has slightly more scores at the extremes
C)it has an extra hump (i.e., bimodal)
D)it does not differ

Question 36

The estimated population variance is:

A)the sum of squared deviation scores divided by N
B)the sum of squared deviation scores divided by N - 1
C)the sum of squared deviation scores divided by N - standard deviation
D)the sum of squared deviation scores minus 1

Question 37

It takes a slightly __________ sample mean to get a significant result when using a t distribution than when using a normal curve.

A)more negative
B)less extreme
C)more extreme
D)more exact

Question 38

If 15 research participants take a pretest and a posttest with a mean change score of 1.5, and if the standard deviation of the comparison distribution is .5, what is the t score?

A)1.5/(15 - 1)= .11
B)1.5/15 = .10
C)1.5/.5 = 3.00
D)15/1.5 = 10

Question 39

There is an entire family of t distributions that vary in shape according to the degrees of freedom used to estimate the population variance. However, for any particular degrees of freedom, there is/are only _____ t distribution (s).

A)0
B)1
C)2
D)3

Question 40

In a study with 10 degrees of freedom, what would be your cutoff score for a t distribution using a one-tailed test at the .05 level of significance?

A)1)372
B)1)813
C)2)764
D)2)228

Question 41

The estimated effect size for a study using a t test for dependent means is the mean of the difference scores divided by the:

A)difference scores
B)estimated variance of the sample of difference scores
C)estimated standard deviation of the population of difference scores
D)estimated mean of the population of difference scores

Question 42

Which of the following poses a serious problem when using a t test for dependent means, one-tailed?

A)The population of difference scores is even moderately different from normal.
B)The sample has less than 40 participants.
C)There is a ceiling effect in the test, which is likely to make the population of difference scores highly skewed.
D)Pretest and posttest scores are highly correlated with each other.

Question 43

For the following question(s): A school counselor claims that he has developed a technique to reduce prestudying procrastination in students. He has students time their procrastination for a week and uses this as a pretest (before)indicator of procrastination. Students then attend a workshop in which they are instructed to do a specific warming-up exercise for studying by focusing on a pleasant activity. For the next week, students again time their procrastination. The counselor then uses the time from this week as the posttest (after)measure.
Suppose the counselor wants to examine whether there is a change of any kind (either an increase or decrease)in procrastination after attending his workshop. What would be the appropriate description of "Population 2" (the population to which the population his sample represents is being compared)?

A)People whose posttest scores will be lower than their pretest scores
B)People whose change scores will be greater than 0
C)People whose change scores will be 0
D)People whose change scores will be less than their pretest scores

Question 44

Which of the following is an assumption or requirement within the logic and mathematics of the t test?

A)A sample of more than 50 people
B)A normal population
C)A normal sample
D)A mean change score that is greater than 10

Question 45

With a t test for dependent means, Population 2 will ordinarily have a mean of:

A)-1
B)0
C)+1
D)it varies from sample to sample

Question 46

What type of research design would be expected to yield the highest amount of power (assuming studies with the same sample size)?

A)A study using a Z test
B)A study using a t test
C)A study using a single-sample design
D)A study using a repeated-measures design

Question 47

When utilizing t tests, __________ would be considered an adequate amount of power.

A)40%
B)50%
C)65%
D)80%

Question 48

Suppose a researcher conducted a t test for dependent means using scores from pairs of research participants (i.e., mothers and sons). The researcher considered each pair as if it were one person and calculated a difference score for each pair. In this example, the t test could also be called a:

A)t test for matched pairs
B)t test for unmatched pairs
C)t test for mixed pairs
D)t test for independent pairs

Question 49

For the following question(s): A researcher conducts a t test for dependent means in which it is predicted that there will be a decrease in unemployment from before to after a particular job-skills training program. The cutoff t needed is -1.833. The standard deviation of the distribution of means of change scores is 2.0 and the mean change score for the sample studied is an increase of 5.2.

-What is the effect size?

A)5)2/-1.833 = -2.84; large
B)2/5.2 = .38; approximately medium
C)5)2/2 = 2.60; large
D)It cannot be determined without also knowing the population standard deviation

Question 50

For a research study that utilized a t test for dependent means, an effect size of -.98 would be considered:

A)small
B)medium
C)large
D)very large

Question 51

For the following question(s): A school counselor claims that he has developed a technique to reduce prestudying procrastination in students. He has students time their procrastination for a week and uses this as a pretest (before)indicator of procrastination. Students then attend a workshop in which they are instructed to do a specific warming-up exercise for studying by focusing on a pleasant activity. For the next week, students again time their procrastination. The counselor then uses the time from this week as the posttest (after)measure.

-Presume the counselor wants to examine whether there is a change (either an increase or decrease)in procrastination after attending his workshop. If the counselor tests 10 students using the .05 level of significance, what cutoff t score(s)will he use? (You should be able to figure this out without a table.)

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

Question 52

What is considered a medium effect size for a t test for dependent means?

A) .20
B) .30
C) .50
D) .80

Question 53

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 54

For the following question(s): A researcher conducts a t test for dependent means in which it is predicted that there will be a decrease in unemployment from before to after a particular job-skills training program. The cutoff t needed is -1.833. The standard deviation of the distribution of means of change scores is 2.0 and the mean change score for the sample studied is an increase of 5.2.

-What is the t score?

A)5)2/-1.833 = -2.84
B)2/5.2 =. 38
C)5)2/2 = 2.60
D) /5.2 = .77

Question 55

For the following question(s): A school counselor claims that he has developed a technique to reduce prestudying procrastination in students. He has students time their procrastination for a week and uses this as a pretest (before)indicator of procrastination. Students then attend a workshop in which they are instructed to do a specific warming-up exercise for studying by focusing on a pleasant activity. For the next week, students again time their procrastination. The counselor then uses the time from this week as the posttest (after)measure.
A researcher conducts a t test for dependent means with 10 participants. The estimated population variance of the change scores is 20. What is the variance of the distribution of the means of change scores?

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

Question 56

Why do studies using difference scores tend to have larger effect sizes than studies using other research designs?

A)There is a 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)Because participants provide their own baseline, variance becomes a wildcard, causing the effect size to increase.
D)Because studies with dependent means usually use a large number of participants, larger effect sizes are easily detected.

Question 57

What is often a limitation of research using a repeated-measure design?

A)low power
B)lack of control group
C)low standard deviation of difference scores
D)all of the above

Question 58

Power for a t test for dependent means can be determined using:

A)a power software package
B)an Internet power calculator
C)a power table
D)any of the above

Question 59

For the following question(s): A school counselor claims that he has developed a technique to reduce prestudying procrastination in students. He has students time their procrastination for a week and uses this as a pretest (before)indicator of procrastination. Students then attend a workshop in which they are instructed to do a specific warming-up exercise for studying by focusing on a pleasant activity. For the next week, students again time their procrastination. The counselor then uses the time from this week as the posttest (after)measure.
Suppose the counselor found the sum of squared deviations from the mean of the sample to be 135. Given that he tested 10 people, what would be the estimated population variance?

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

Question 60

For the following question(s): A researcher conducts a t test for dependent means in which it is predicted that there will be a decrease in unemployment from before to after a particular job-skills training program. The cutoff t needed is -1.833. The standard deviation of the distribution of means of change scores is 2.0 and the mean change score for the sample studied is an increase of 5.2.

-What is the appropriate conclusion?

A)Reject null hypothesis
B)Do not reject null hypothesis
C)It cannot be determined without also knowing the population mean
D)It cannot be determined without also knowing the population SD or its estimate

Question 61

The variance of a sample is a(n)__________ estimator of the population variance.

Question 62

One can figure an unbiased estimate of the population variance by dividing the sum of squared deviation scores by __________.

Question 63

What is the approximate power for a study using the t test for dependent means with an expected small effect size (.20), two-tailed test, N = 40?

A)19
B)24
C)55
D)nearly 1

Question 64

The estimate of a population parameter that is likely systematically to overestimate or underestimate the true value of the population parameter is known as a __________.

Question 65

Approximately how many research participants would be required for 80% power for a study using the t test for dependent means (assume a one-tailed hypothesis with an expected medium effect size of .50):

A)12
B)26
C)33
D)196

Question 66

Degrees' of freedom is calculated as the number of scores minus the mean. (True or False)

Question 67

Student's t was created by __________.

Question 68

A research article reports results of a study using a t test for dependent means as "t(38)= 3.11, p < .01." This tells you:

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

Question 69

If not otherwise indicated, one should assume that researchers utilized a __________ test.

A)one-tailed
B)two-tailed
C)whole sample
D)partial sample

Question 70

A t test is a hypothesis-testing procedure used when the population variance is unknown. (True or False)

Question 71

A research article reports results of a study using a t test for dependent means as "t(16)= 2.67, p < .05." This tells you:

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

Question 72

What can be said about the "Independence" difference score?

A)It is not statistically significant.
B)It is statistically significant at the .05 level.
C)It is statistically significant at the .01 level.
D)It is statistically significant at the .10 level.

Question 73

Which of the following is the most likely way for results of a t test for dependent means to be presented in a research article for a study with 25 participants?

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

Question 74

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

Question 75

Hypothesis testing in which a sample mean is being compared to a known population mean but the population variance is unknown is called a __________.

Question 76

For the following question(s): A research article included the following table:
Mean Score on Four Questionnaire Scales Before and After the Experimental Manipulation
Questionnaire Before After Change
Dominance 18.42 16.31 -2.11
Independence 17.25 21.38 4.13**
Conformity 18.97 17.20-1.77*
Nurturance 16.11 13.89 -2.22*
______________________
*p < .05; **p < .01

-Which of the following is most likely to be true given the information on this table?

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

Question 77

Approximately how many research participants would be required for 80% power for a study using the t test for dependent means (assume a two-tailed hypothesis with an expected small effect size of .20):

A)156
B)196
C)26
D)33

Question 78

For the following question(s): A research article included the following table:
Mean Score on Four Questionnaire Scales Before and After the Experimental Manipulation
Questionnaire Before After Change
Dominance 18.42 16.31 -2.11
Independence 17.25 21.38 4.13**
Conformity 18.97 17.20-1.77*
Nurturance 16.11 13.89 -2.22*
______________________
*p < .05; **p < .01

-Which of the following differences was NOT statistically significant?

A)dominance
B)independence
C)conformity
D)nurturance

Question 79

In a study the sum of squared deviations from the mean for the sample is 12 and there are 4 participants. What is the estimated population variance?

Question 80

What is the approximate power for a study using the t test for dependent means with an expected large effect size, one-tailed and N = 50?

A)40
B)77
C)88
D)nearly 1