Deck 13: Paired and Independent-Samples T Tests

Question 1

Two researchers measure attitudes toward capital punishment in the year 2000 and again in the year 2005. One researcher uses a panel study design (the same persons are questioned in 2000 and in 2005); the other uses a trend study design (different samples from the population are questioned in 2000 and 2005). In analyzing the data that was collected,

A) both researchers should use paired-sample t tests
B) both researchers should use independent-samples t tests
C) the panel study researcher should use paired-sample t tests but the trend study researcher should use independent-samples t tests
D) the panel study researcher should use independent-samples t tests but the trend study researcher should use paired-samples t tests

Answer 1

the panel study researcher should use paired-sample t tests but the trend study researcher should use independent-samples t tests

Question 2

You are testing a two-tailed hypothesis. Your SPSS output tells you that the two-tailed significance level of a particular t statistic is .01. What is the probability of making a Type I error if you reject the null hypothesis?

A) .99
B) .05
C) .01
D) cannot be determined

Answer 2

.01

Question 3

Which would be an appropriate statistical procedure to test the hypothesis that Americans listen to radio an average of 200 minutes a day?

A) independent-samples t test
B) one-sample t test
C) paired-samples t test

Answer 3

one-sample t test

Question 4

You are doing a paired-samples t test with 694 valid cases. How many degrees of freedom will the t test have?

A) 692
B) 693
C) 694
D) 695

Question 5

Without computing any new variables, which would be an appropriate statistical procedure to test the hypothesis that, on average, college students listen to less radio than they did when they were high school students?

A) independent-samples t test
B) one-sample t test
C) paired-samples t test

Question 6

You are doing a paired-samples t test. What level of measurement is required on the variables you are using?

A) They must be nominal.
B) They must be ordinal.
C) They must be interval/ratio.
D) They can be any level of measurement.

Question 7

What is the largest risk of making a Type I error that social scientists will usually take?

A) 5% chance
B) 68% chance
C) 95% chance
D) 99.7% chance

Question 8

An author reports the following information about a two-tailed paired-samples t test: t = 5.43, df = 83, p = .001. Which of the following is true?

A) There were 82 valid cases.
B) The null hypothesis was rejected
C) The two means were not significantly different.
D) All of the above are true.

Question 9

Which of the following correctly describes a Type I error?

A) not rejecting a null hypothesis that is false
B) not rejecting a null hypothesis that is true
C) rejecting a null hypothesis that is false
D) rejecting a null hypothesis that is true

Question 10

Which of the following hypotheses should be tested using a paired-samples t test?

A) The average posttest score was 78.
B) Women had the same average pretest score as men.
C) On average, persons' posttest scores were the same as their pretest scores.
D) Pretest and posttest scores were not correlated.

Question 11

For an independent-samples t test, the test variable (the variable whose values will be averaged for each group) can be what level of measurement?

A) only interval/ratio
B) either interval/ratio or ordinal
C) interval/ratio, ordinal, or nominal

Question 12

Any paired-samples t test could also be tested as a(n)

A) crosstab
B) independent-samples t test
C) multiple regression
D) one-sample t test

Question 13

Your independent-samples t test research hypothesis is that, when asked the ideal number of children to have, men report a higher average than women. The following results are consistent with the _____ and you proceed to _____.
 

A) null hypothesis … Step 3 (check significance level)
B) null hypothesis … Step 4 (state conclusion)
C) research hypothesis … Step 3 (check significance level)
D) research hypothesis … Step 4 (state conclusion)

Question 14

You are doing a two-tailed paired-samples t test and your results are statistically significant. The phrase "statistical significance" means the same as which of the following?

A) There is a large difference between the means in the population.
B) There is an important difference between the means in the population.
C) You are willing to reject the claim that there is no difference between the means in the population.
D) You are NOT willing to reject the claim that there is no difference between the means in the population.

Question 15

Which of the following hypotheses should be tested using an independent-samples t test?

A) The average posttest score was 78.
B) Women had the same average pretest score as men.
C) On average, persons' posttest scores were the same as their pretest scores.
D) Pretest and posttest scores were not correlated.

Question 16

An author reports the following information about a one-tailed independent-samples t test: t = 1.71, df = 17, p = .111. The sample means were consistent with the research hypothesis. Which of the following is true?

A) The two-tailed significance level must have been .222.
B) The null hypothesis was rejected
C) The two groups were significantly different.
D) All of the above are true.

Question 17

For an independent-samples t test, the grouping variable (the variable whose attributes are used to identify the two groups to be compared) can be what level of measurement?

A) only interval/ratio
B) either interval/ratio or ordinal
C) interval/ratio, ordinal, or nominal

Question 18

Your paired-samples t test research hypothesis is that, on average, persons wish they had fewer children (KIDSBEST) than they actually have (CHILDREN). The following results are consistent with the _____ and you proceed to _____.
 

A) null hypothesis … Step 3 (check significance level)
B) null hypothesis … Step 4 (state conclusion)
C) research hypothesis … Step 3 (check significance level)
D) research hypothesis … Step 4 (state conclusion)

Question 19

If the significance level of Levene's Test is.050 or less,

A) you cannot test the null hypothesis as an independent-samples t test
B) you ignore the significance level of the t test, go to Step 4, and reject the null hypothesis
C) you use the upper line of results (Equal variances assumed)
D) you use the lower line of results (Equal variances not assumed)

Question 20

You are testing a one-tailed paired-samples t test hypothesis. The sample means were consistent with the research hypothesis. Based on the following results, the significance level is _____ and you _____ the null hypothesis.
 

A) .056 … do not reject
B) .112 … do not reject
C) .112 … reject
D) .224 … do not reject

Question 21

If the mean IQ of a sample of right-handed persons is significantly higher than the mean IQ of a sample of left-handed persons, then which of the following must be true?

A) All right-handed persons must have higher IQs than all left-handed persons.
B) Most right-handed persons must have higher IQs than most left-handed persons.
C) The median IQ of right-handed persons must be higher than the median IQ of left-handed persons.
D) None of the above must be true.

Question 22

Independent-samples t tests compare means for how many variables for how many groups of cases?

Question 23

Write a research hypothesis and its companion null hypothesis that could be tested with a paired-samples t test.

Question 24

If the significance of Levene's test is greater than .05, are "equal variances assumed" or "equal variances not assumed" for the independent-samples t test?

Question 25

What kinds of questions can you answer using an independent-samples t test?

Question 26

Which of the following correctly describes a Type II error?

A) not rejecting a null hypothesis that is false
B) not rejecting a null hypothesis that is true
C) rejecting a null hypothesis that is false
D) rejecting a null hypothesis that is true

Question 27

Paired-samples t tests compare means for how many variables for how many groups of cases?

Question 28

Which would be an appropriate statistical procedure to test the hypothesis that, on average, Democrats listen to more radio than Republicans?

A) independent-samples t test
B) one-sample t test
C) paired-samples t test

Question 29

Which one of the following is NOT a correct description of the number obtained at Step 3 in hypothesis testing?

A) the probability of making a Type I error if you reject the null hypothesis
B) the probability of making a Type II error if you do not reject the null hypothesis
C) the probability of getting the sample results you got if the null hypothesis is true
D) the significance level

Question 30

When does a researcher risk making a Type II error?

Question 31

You are testing a one-tailed independent-samples t test hypothesis. The sample results are consistent with the research hypothesis. Based on the following results, the significance level is _____ and you _____ the null hypothesis.
 

A) .701 … do not reject
B) .698 … do not reject
C) .3505 … do not reject
D) .349 … do not reject

Question 32

Why are paired samples called that?

Question 33

Can two frequency distributions substantially overlap if their means are significantly different? Explain.

Question 34

What kinds of questions can you answer using a paired-samples t test?

Question 35

A researcher does a paired-samples t test with 39 cases. How many degrees of freedom does the t test have? __________

Question 36

A researcher has done a paired-samples t-test. She reports the test's degrees of freedom to be 100. How many cases were there in the sample? __________

Question 37

When does a researcher risk making a Type I error?

Question 38

Write a research hypothesis and its companion null hypothesis that could be tested with an independent-samples t test.

Question 39

Does statistical significance indicate substantive importance? Explain.

Question 40

Why are independent samples called that?

Question 41

Answer the questions that follow this SPSS output:


"Your research hypothesis is "In the population, persons' mothers average more years of schooling than do their fathers." (¯EDUCMOM>¯EDUCDAD)

A) State the null hypothesis being tested.
B) Is this a one-tailed or two-tailed hypothesis?
C) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
D) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
E) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
F) Are your results statistically significant? (yes / no)

Question 42

Answer the questions that follow this SPSS output:


Your research hypothesis is "In the population, there is a difference in the average SAT scores of persons who attended small high schools and persons who attended large high schools." (¯EDUCMOM≤¯EDUCDAD)

A) State the null hypothesis being tested.
B) Is this a one-tailed or two-tailed hypothesis?
C) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
D) What is the significance level? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
E) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
F) Are your results statistically significant? (yes / no)

Question 43

Answer the questions that follow this SPSS output:


Your research hypothesis is "In the population, the average number of hours of TV watched is less than the average number of hours spent using the Internet." ((TVHOURS) ̅<(WEBHRS) ̅)

A) State the null hypothesis being tested.
B) Is this a one-tailed or two-tailed hypothesis?
C) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
D) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
E) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
F) Are your results statistically significant? (yes / no)

Question 44

Answer the questions that follow this SPSS output:


Your research hypothesis is "In the population, restaurants' average health inspection score in 2006 (HEALTHSCORE06) was higher than the average for those same restaurants in 2005 (HEALTHSCORE05)". (¯HEALTHSCORE06>¯HEALTHSCORE05)

A) State the null hypothesis being tested.
B) Is this a one-tailed or two-tailed hypothesis?
C) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
D) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
E) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
F) Are your results statistically significant? (yes / no)

Question 45

Answer the questions that follow this SPSS output:

Your research hypothesis is "In the population, persons with 16 years of schooling average more children than persons with 20 years of schooling." ( )

A) State the null hypothesis being tested.
B) Is this a one-tailed or two-tailed hypothesis?
C) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
D) What is the significance level? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
E) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
F) Are your results statistically significant? (yes / no)

Question 46

Answer the questions that follow this SPSS output:

Your research hypothesis is "In the population, the average number of hours spent using the Internet by full-time workers is greater than by part-time workers." (¯HEALTHSCORE06≤¯HEALTHSCORE05)

A) State the null hypothesis being tested.
B) Is this a one-tailed or two-tailed hypothesis?
C) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
D) What is the significance level? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
E) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
F) Are your results statistically significant? (yes / no)

Question 47

Answer the questions that follow this SPSS output:


Your research hypothesis is "On average, persons in the population with 16 years of schooling have less general knowledge (GENKNOW) than persons with 20 years of schooling." (¯(〖GENKNOW〗_16 )<¯(〖GENKNOW〗_20 ) )

A) State the null hypothesis being tested.
B) Is this a one-tailed or two-tailed hypothesis?
C) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
D) What is the significance level? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
E) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
F) Are your results statistically significant? (yes / no)

Question 48

Whenever you reject a null hypothesis, you may be making a correct decision or you may be making a Type ___ error; whenever you do not reject a null hypothesis, you may be making a correct decision or you may be making a Type _____ error.

Question 49

Answer the questions that follow this SPSS output:

Your research hypothesis is "In the population, the average on the POSTTEST is higher than the average on the PRETEST." ( (POSTTEST) ̅>(PRETEST) ̅)

A) State the null hypothesis being tested.
B) Is this a one-tailed or two-tailed hypothesis?
C) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
D) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
E) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
F) Are your results statistically significant? (yes / no)