Question 1

The following are the scores for the same five individuals obtained under both experimental and control conditions:
   Test  against  > 0 ($\alpha$ = .05) and draw final conclusions.

Accepted Answer

retain  ; the results are not strong enough to conclude that there is a difference.

Question 2

We wish to compare reaction time to sound with reaction time to light. In a carefully controlled experiment, the time required to react to a buzzer and the time required to react to a white signal light are obtained for each of six subjects. The following are the results (in milliseconds): 
  Set up the statistical hypotheses; perform the test (α = .05), and draw final conclusions.

Accepted Answer

reject 
  
; conclude 
  
 reaction time is longer to the light.

Question 3

A tire manufacturer wishes to compare two designs for fiberglass belted tires with regard to tread wear. One tire of each design is placed on the rear wheels of each of seven test automobiles that are inspected regularly. The elapsed mileage until replacement is necessary is recorded for each tire. The following are the results (to the nearest 1000 miles):
  Set up the statistical hypotheses; perform the test (α = .05) and draw final conclusions.

Accepted Answer

retain 
  
; the evidence is insufficient to conclude that there is a difference in tread wear.

Question 4

You wish to compare two different orders of presentation (A and B) of the items on a standard IQ test administered to a  representative group of 10-year-olds. The test is constructed to give a standard deviation of 15 IQ points in a representative group at any age level. What is the probability of detecting a true difference ( 
of 5 IQ points (two-tailed test, ) if each of the two samples is of size:
 
(a)10?
(b)20?
(c)40?
(d)80?
(e)200?

Accepted Answer

The answer of You wish to compare two different orders...

Question 5

Observations are dependent when
A) the same subjects have been used for both sets of observations
B) subjects have been matched on some variable related to the variable observed
C) either of the above is true
D) the mean of X exactly equals the mean of Y

Accepted Answer

Observations are dependent when either the same subjects are used for both sets of observations or when subjects are matched on some variable related to the variable observed.

Question 6

When samples are dependent, the standard error of the difference between two means will be
A) larger than when samples are independent
B) smaller than when samples are independent
C) smaller or larger than otherwise, but we cannot predict which
D) unaffected

Accepted Answer

When samples are dependent, the standard error of the difference between two means is typically smaller because the variability due to individual differences is reduced, as the same subjects are used in both conditions.

Question 7

When samples are dependent, this affects the
A) choice of null hypothesis
B) choice of alternative hypothesis
C) mean of the sampling distribution
D) standard deviation of the sampling distribution

Accepted Answer

When samples are dependent, it affects the standard deviation of the sampling distribution because the variability is influenced by the correlation between the samples.

Question 8

The test between two dependent means requires that one must take special account of
A) the correlation between the two sets of measures
B) the standard deviation of the two variables
C) the case of equal sample size
D) the assumption of normality

Accepted Answer

The test between two dependent means, such as a paired t-test, requires accounting for the correlation between the two sets of measures because the observations are related or paired.

Question 9

Using paired observations (dependent observations) is most advantageous when
A) sample size is unequal
B) standard deviations must be estimated from samples
C) the correlation between the pairs of scores is high
D) the correlation between the pairs of scores is low

Accepted Answer

Using paired observations is most advantageous when the correlation between the pairs of scores is high because it allows for more accurate estimation of the treatment effect by accounting for the variability between pairs.

Question 10

For which of the following would the samples be considered dependent? A study to compare
A) husbands and their wives with regard to political attitudes
B) current freshmen and freshmen 10 years ago, all of whom are (were) psychology majors, with regard to SAT scores
C) current freshmen and freshmen 10 years ago (a mixture of many academic majors) with regard to SAT scores
D) none of the above involve dependent samples

Accepted Answer

In option A, the samples are dependent because the political attitudes of husbands and their wives are likely to be related or influenced by each other, making them paired or matched samples.

Question 11

We wish to test the hypothesis of no difference between two means. We will use either two matched groups of 40 subjects each, or else two independent groups of 40 subjects each. When the outcome is evaluated at the 5% significance level, the critical value of t will be
A) larger if dependent samples are used
B) the same in either situation
C) larger for one method than for the other, but we cannot tell which from the information given
D) smaller if dependent samples are used

Accepted Answer

In a matched or dependent samples t-test, the degrees of freedom are typically smaller, leading to a larger critical value of t compared to independent samples with the same number of subjects.

Question 12

We wish to test the hypothesis of no difference between the means of two dependent groups. There are 30 cases in the first sample, and 30 cases in the second. The number of degrees of freedom for this test will be
A) 28
B) 29
C) 58
D) 59

Accepted Answer

For dependent groups, the degrees of freedom is calculated as the number of pairs minus one. Since there are 30 pairs, the degrees of freedom is 30 - 1 = 29.

Question 13

We plan to use the D score approach to test the difference between two means for a sample of 10 matched pairs. Once the D scores are computed, the procedure is identical to that for testing a hypothesis about
A) the difference between two independent means
B) a single mean
C) the difference between two dependent means
D) the procedure, although similar, is not identical to any of the above

Accepted Answer

The D score approach for matched pairs involves computing the differences and then testing the hypothesis about the mean of these differences, which is similar to testing a hypothesis about a single mean.

Question 14

We plan to use the D score approach for dependent samples to test a hypothesis about the difference between two means. The following are the observations for our three matched pairs:  
A) 9
B) 12
C) 14
D) 16

Accepted Answer

The answer of We plan to use the D score...

Question 15

Which of the following is correct with regard to the use of matched groups as a method of experimental control?
A) We can assure control over any irrelevant variable that might affect the results
B) We may "match out" too much or too little
C) Matching should be used instead of random assignment where possible in order to assure more precise control
D) Through matching we can usually compensate for any inadequacies in our research design

Accepted Answer

Matching can lead to over-matching or under-matching, which can affect the validity of the experiment.

Question 16

A problem in the interpretation of a significant outcome in the test of the difference between two dependent means is particularly likely to occur when
A) population standard deviations are estimated from samples
B) sample size is large
C) a large value of t is obtained
D) members of a pair are not assigned at random to treatment conditions

Accepted Answer

When members of a pair are not assigned at random to treatment conditions, it can lead to confounding variables affecting the results, making it difficult to interpret the significance of the outcome.

Question 17

Which kind of test of the difference between two means, if any, is most likely to present problems in interpretation?
A) independent random samples test
B) matched samples test
C) repeated measures (on the same subjects) test
D) all are equal in this respect

Accepted Answer

Repeated measures tests can present problems in interpretation due to issues like carryover effects, where the first measurement influences the second, and other within-subject variability factors.

Question 18

An order effect occurs when
A) one group is given the first treatment, and the other is subsequently given the other treatment
B) one group is used, but the first treatment has no influence upon the second
C) two groups are used, and the first group is treated first and the second group treated next
D) the same subjects are used for both groups, and the treatment given first changes performance on the treatment given second

Accepted Answer

Order effects occur when the sequence in which treatments are administered affects the outcome, as in option D where the first treatment influences the performance on the second treatment.

Quiz 15: Testing for a Difference

The following are the scores for the same five individuals obtained under both experimental and control conditions: Test against > 0 ( α\alphaα = .05) and draw final conclusions.

Observations are dependent when

When samples are dependent, the standard error of the difference between two means will be

When samples are dependent, this affects the

The test between two dependent means requires that one must take special account of

Using paired observations (dependent observations) is most advantageous when

For which of the following would the samples be considered dependent? A study to compare

We wish to test the hypothesis of no difference between two means. We will use either two matched groups of 40 subjects each, or else two independent groups of 40 subjects each. When the outcome is evaluated at the 5% significance level, the critical value of t will be

We wish to test the hypothesis of no difference between the means of two dependent groups. There are 30 cases in the first sample, and 30 cases in the second. The number of degrees of freedom for this test will be

We plan to use the D score approach to test the difference between two means for a sample of 10 matched pairs. Once the D scores are computed, the procedure is identical to that for testing a hypothesis about

We plan to use the D score approach for dependent samples to test a hypothesis about the difference between two means. The following are the observations for our three matched pairs:

Which of the following is correct with regard to the use of matched groups as a method of experimental control?

A problem in the interpretation of a significant outcome in the test of the difference between two dependent means is particularly likely to occur when

Which kind of test of the difference between two means, if any, is most likely to present problems in interpretation?

An order effect occurs when