Deck 14: Testing Hypotheses About the Difference Between Two Independent Groups

Question 1

We wish to determine if two strains of laboratory rats differ in maze-running ability. Random samples of naive (never been experimented on) rats are selected from each strain, and each rat is run through a test maze until it can negotiate the maze with no errors on two consecutive trials. The following results are obtained (number of trials to learn):

(a)  Set up

and

. 
(b) Perform the test (α = .05) 
(c)  Draw final conclusions.

Answer 1

(a)  
(b)
   
(c) retain ; sample difference is not sufficient to warrant that the two strains differ.

Question 2

We are screening drugs for possible use against cancer. We implant 11 laboratory mice with cancer cells. Five of them selected at random are treated with Theron-P. Two months later, detectable tumors are removed from all 11 animals and weighed. The following are the results (in grams):

(a) Set up

and

.
(b)Perform the test ( $\alpha$ = .05)
(c) Draw final conclusions.

Answer 2

(a)
(b)

(c) reject ; Theron-P is effective in reducing the size of cancerous tumors in mice.

Question 3

The makers of Streamer automobiles wish to compare two possible carburetors for use in their larger V-6 model with regard to gasoline consumption. Eight new Streamers with V-6 engines are randomly divided into two groups. One group has Type L carburetors installed and the other, Type M carburetors. The following are the results of standard city mileage tests on the Streamers (in mpg):
Set up

and
; perform the test ( $\alpha$ = .05), and draw final conclusions.

Answer 3

(a)?

?
(b)?

(c)? reject

; type L carburetors are more fuel efficient.

Question 4

We wish to compare the marriage counselors from two different clinics with regard to how often couples they have counseled seek a divorce. As many as possible of the couples counseled by each of the counselors are located. The following are the percentages for each counselor of client couples who obtained, or were seeking, a divorce one year after termination of counseling:
Set up the appropriate statistical hypotheses; perform the test ( $\alpha$ = .05); and draw final conclusions.

Question 5

You read in a popular new magazine "A group of college women scored significantly higher, on the average, than a group of college men on the specially constructed test of intuitive problem solving."
(a)How is the statistically unsophisticated person likely to interpret the above statement (consider in particular the italicized phrase)?
(b)What does the statement really mean? Answer in terms of what was tested and what was decided.
(c)Is it possible that the difference in means between the women and men was in fact quite small? If so, how could a significant difference be observed?
(d)What additional statistical information would you want in order to evaluate the difference between the women and the men?

Question 6

Given the following information about the two populations, compute d, 
(a)   
(b)   
(c)

Question 7

Calculate the different measures of effect size, g and r, for the results in Problem 4

Question 8

You plan to perform an experiment and conduct a two-tailed test of
( $\alpha$ = .05).

Suppose that in fact
How many times out of 100 repetitions of your experiments would you expect to obtain significant results if you use samples of size:
(a)8(b) 15 (c)45(d)110

Question 9

You plan to conduct a two-tailed test of ( $\alpha$ = .05).using samples of size

What is the probability of detecting a d of:
(a).1(b).2(c).3(d).5(e)1
What do the answers to this problem suggest about using samples of this size?

Question 10

The test of the difference between two means involves comparison of means of

A) the same variable under the same conditions
B) the same variable under different conditions
C) different variables under the same conditions
D) different variables under different conditions

Question 11

The hypothesis testing procedures for comparing means of independent samples would be inappropriate for comparing

A) achievement scores of a sample taught by method A with those of a sample taught by method B
B) coordination scores of a sample of volunteers on the first trial with their scores on the second trial
C) sociability scores of a sample of psychology majors with those of a sample of sociology majors
D) maze running scores of a sample of albino rats with those of a sample of Norwegian rats

Question 12

The exact nature of the random sampling distribution of differences between two means is dependent on

A) sample size
B)
C) both of the above
D) none of the above

Question 13

In testing the difference between two means, the total of sample size is, in general, used most efficiently when

A) and are as discrepant as possible
B)
is 4 times the size of (or vice versa)
C) is 2 times the size of (or vice versa)
D)

Question 14

The central limit theorem is of assistance for the sampling distribution of

A) single means only
B) differences between two means only
C) both of the above
D) single means to a great extent, and differences between two means to a small extent

Question 15

In testing the difference between two means, a one-tailed test would be appropriate when

A) previous experience shows that one condition tends to produce better performance than the other
B) reason clearly suggests that one condition should produce better performance than the other
C) a finding of a difference in the opposite direction would be no different to the experimenter than a finding of no difference at all
D) any of the above conditions exist

Question 16

Suppose that X and Y stand for scores on a test of learning under conditions of reward and punishment, respectively. If we are interested only in whether reward results in higher scores than punishment, and obtain the difference between the two conditions in terms of
, we should place the region of rejection

A) entirely in the right tail of the sampling distribution
B) entirely in the left tail of the sampling distribution
C) half in one tail and half in the other
D) in the center of the sampling distribution

Question 17

In testing a hypothesis about the difference between two means, the probability of rejecting
(when there is a difference) is increased when

A)
B)
C) both and are small
D) both and
are large

Question 18

The variance estimate made by pooling data from two samples is calculated by

A)
B)
C)
D)

Question 19

The assumption of homogeneity of variance means that

A) the scores in the two populations are homogeneous in that they show little variability
B) the scores in the two populations are equally variable
C) the scores in the two samples are homogeneous in that they show little variability
D) the scores in the two samples are equally variable

Question 20

Combining data from two samples to make a pooled variance estimate is logically justified when

A) the two n's are equal
B) the two n's are unequal
C) it can be assumed that the two population standard deviations are equal
D) it can be assumed that the two population standard deviations are unequal

Question 21

We wish to test the hypothesis of no difference between the means of two independent samples. The first sample consists of 30 cases and the second consists of 20 cases. The number of degrees of freedom for the test is

A) 25
B) 48
C) 49
D) 50

Question 22

To test the null hypothesis of no difference between two means, we calculate the statistic

A)
B)

C)
D)

Question 23

If some fact of an experiment results in a smaller standard error of the difference between two means than otherwise, this is

A) undesirable, because it will make it less likely to claim a difference when one exists
B) undesirable, because it makes it more likely to claim no difference when there is a difference
C) desirable, because it makes it more likely to claim a difference when one exists
D) desirable, because it makes it less likely to claim a difference when there is none

Question 24

Suppose that
The mean of a sampling distribution of for samples drawn from these populations would equal

A) +5
B) 0
C) -5
D) cannot tell from the information given

Question 25

Samples of size 12 and 10 are selected from populations 1 and 2, respectively. The sample results give Our best pooled estimate of
is

A) 8.6
B) 9.5
C) 17.1
D) 12.2

Question 26

The scores from two randomly selected samples from populations A and B are as follows: A: 2, 4,B: 3, 5.The pooled variance estimate,
would equal

A) 2
B) 1
C) 4
D) 3

Question 27

Professor Jones performs a t test of using and finds a significant difference between
and
From this we can infer

A) a large difference between
and
B) an important difference between and
C) and to be unequal
D) all of the above

Question 28

When using a t test to analyze the results of an experiment using college sophomore volunteers, the assumption of random sampling

A) is fulfilled if a random procedure is used to assign subjects to treatment groups
B) places strict limits on all generalizations
C) places strict limits on statistical generalizations
D) all of the above

Question 29

As used in most behavioral science experiments, statistical inference procedures do not provide us with

A) the authority to make inferences beyond our particular set of conditions and type of subjects
B) a means of accounting for chance sampling variations in our particular sample results
C) a means of determining the kinds of results that would be expected as a result of chance factors
D) they provide us with all of the above

Question 30

In a two-group experiment, random assignment

A) insures lack of bias in the experiment
B) insures lack of bias in the long run
C) insures equality of the two groups
D) is important solely for statistical reasons

Question 31

Random sampling and random assignment

A) are synonymous
B) often amount to the same thing
C) are different procedures
D) can be substituted for each other

Question 32

Suppose that Suppose also that the effect size Thus, must equal

A) 28
B) 29
C) 32.2
D) 26.4

Question 33

The effect size d is

A) .25
B) .75
C) .67
D) .33