Deck 10: The Hypothesis of Difference

Question 1

In order to calculate the estimated standard error of difference, all that need be known is (are)

A) the means of the two samples
B) the sizes of the two samples
C) the standard deviation of the two samples
D) the standard errors of the mean for each of the two samples

Answer 1

the standard errors of the mean for each of the two samples

Question 2

10-16. When pairs of samples are selected from two separate populations, the mean of the distribution of differences is assumed to be

A) some value other than zero
B) zero
C) a constant
D) equal to the mean of the distribution of means

Answer 2

A

Question 3

When the difference between pairs of randomly selected means are obtained, the resulting distribution is called

A) the distribution of means
B) the distribution of differences
C) the distribution of individual sample scores
D) the ogive distribution

Answer 3

B

Question 4

10-15. Regarding the distribution of differences, the assumption of normality is based on

A) Pascal's triangle
B) Gossett's law
C) the Central Limit theorem
D) the Gaussian law

Question 5

The distribution of differences is composed of the differences between

A) raw scores and the mean
B) the highest and lowest scores in a distribution
C) the standard deviation and the standard error of the mean
D) pairs of randomly selected sample means

Question 6

10-11. The estimated standard error of difference is an estimate of

A) centrality
B) variability
C) normality
D) none of these, since the estimated standard error of difference is not a

Question 7

10-14. The distribution of differences is

A) a sampling distribution
B) a distribution of parameters
C) always leptokurtic in shape
D) always platykurtic in shape

Question 8

10-18. In order to ensure a sampling error of zero, each sample must

A) be randomly selected
B) be equal in size
C) be selected from the same population
D) none of these, since one can never assume a sampling error of zero

Question 9

When graphing the distribution of differences, the ordinate is used to represent

A) a sample mean
B) the difference between the mean of the individual raw scores and the sample mean
C) the difference between two sample means
D) frequency of occurrence

Question 10

Whenever the distribution of differences is normally shaped, and all its assumptions are met, then

A) the samples must represent different populations
B) the samples must represent a single population
C) more than two populations must be involved
D) none of these, since when its assumptions are met, the distribution of

Question 11

10-13. When selecting a pair of random-sample means from a single population, the probability of the first mean being higher than the second mean is

A) 1.00
B) 0
C) .50
D) either a or b, but never c

Question 12

10-10. The estimated standard error of difference may be obtained on the basis of the information contained in

A) a single sample
B) a pair of random samples
C) the sampling error
D) a single z score

Question 13

The estimated standard deviation of the distribution of differences is used to predict the

A) standard error of the mean
B) standard error of difference
C) standard error of the estimate
D) actual standard score

Question 14

10-17. In order to use the estimated standard error of difference for making probability estimates, both samples must

A) have equal means
B) have unequal means
C) be free of sampling error
D) have similar amounts of variability

Question 15

Whenever the mean of the distribution of differences equals zero, then one can be fairly safe in concluding that

A) the samples probably represent a single population
B) the samples probably represent different populations
C) there was absolutely no sampling error
D) none of these, since the mean can never equal zero

Question 16

10-12. The Central Limit theorem states that the distribution of differences is

A) always based on a pair of samples
B) always based on a single sample
C) a parameter
D) approximately normal in shape

Question 17

When graphing the distribution of differences, the abscissa is used to represent

A) a sample mean
B) the difference between the mean of the individual raw scores and the sample mean
C) the difference between two sample means
D) the frequency of occurrence

Question 18

When all samples are drawn from a single population, the mean of the distribution of differences should approximate

A) zero
B) +1.0
C) -1.0
D) the mean of the distribution of means

Question 19

If the mean of the distribution of differences were to equal -6.00, this would indicate that

A) the standard deviation of the distribution is a function of the range
B) the samples probably represent different populations
C) the samples were probably selected from a single population
D) none of these, since the mean can never be negative

Question 20

If all the possible pairs of sample means were obtained from a single population, the mean of the distribution of differences would be

A) a statistic
B) a parameter
C) identical with the mean of the distribution of means
D) equal to one-sixth of the range

Question 21

Whenever the null hypothesis is rejected, then

A) the alternative hypothesis must also be rejected
B) the alternative hypothesis must be accepted
C) the alternative hypothesis must be tested separately
D) none of these, since the null hypothesis and the alternative hypothesis are

Question 22

The difference between the T score and the t ratio is that

A) the T score always results in a higher value than does the t ratio
B) the T score refers to several sample means, whereas the t ratio only refers to two sample means
C) the T score is used as a measure of individual performance, whereas the t ratio evaluates the possibility of a performance difference between two
Independent groups
D) none of these, since T and t are the same

Question 23

The alternative hypothesis for the independent t test is also called

A) the hypothesis of association
B) the hypothesis of difference
C) the null hypothesis
D) none of these

Question 24

The t test for two independent samples may only be used when

A) the selection of subjects for the first group does not depend in any way on the selection of subjects for the second group
B) the subjects used in the two samples are matched on some relevant variable
C) the same subjects are used twice
D) the degrees of freedom are independent of the sample sizes

Question 25

For the independent t test, the null hypothesis is always stated in terms of

A) the sample means
B) the population means
C) both of these
D) neither of these

Question 26

The independent t ratio may be used to evaluate whether

A) two samples represent a single population
B) two samples represent different populations
C) both of these
D) neither of these

Question 27

The independent t ratio specifies how far the difference between the sample means deviated from

A) an assumed mean of 50, in units of standard deviations
B) an assumed mean of 100, in units of estimated standard errors of difference
C) an assumed mean of zero, in units of estimated standard errors of difference
D) the standard deviation of the population

Question 28

When the alternative hypothesis is accepted, then

A) the sample means are assumed to be equal
B) the population means are assumed to be equal
C) chance is rejected
D) a significant difference has been established

Question 29

For the t ratio, when the null hypothesis is rejected, then

A) the difference is assumed to be significant
B) the difference is assumed to equal zero
C) the difference is assumed to be positive
D) none of these

Question 30

When the degrees of freedom reach infinity, the t distribution

A) becomes identical with the distribution of raw scores
B) gets larger
C) approximates normality
D) cannot be obtained

Question 31

For the independent t test, degrees of freedom are based on

A) the population sizes
B) the sample sizes
C) the number of samples being compared
D) none of these

Question 32

Like the T score, the t ratio is a measure of

A) individual performance
B) how a single sample performed
C) central tendency
D) none of these, since the T score involves a measure of individual

Question 33

The independent t test may be used to evaluate the difference between

A) two sample means
B) two or more sample means
C) the mean and the standard deviation
D) the mean and the variance

Question 34

The statement that the difference between the two population means is zero, represents

A) the Type 1 error
B) the sampling error
C) the alternative hypothesis
D) the null hypothesis

Question 35

For the independent t test, the null hypothesis states that the samples

A) represent a single population
B) represent different populations
C) are of infinite size
D) each have mean scores of zero

Question 36

For the independent t test, the null hypothesis is always

A) a function of sample size
B) a function of variability
C) a function of centrality
D) the same as the "chance" hypothesis

Question 37

When a difference is considered "significant", it indicates that the difference is probably

A) meaningful and profound
B) due to chance and chance alone
C) not due to chance alone
D) none of these

Question 38

For the independent t test, the hypothesis of "no difference" is called the

A) alternative hypothesis
B) null hypothesis
C) central limit hypothesis
D) hypothesis of association

Question 39

When the null hypothesis is rejected, then

A) the "chance" explanation is completely ruled out
B) the "chance" explanation, though not ruled out, becomes improbable
C) the "chance" explanation is fully accepted
D) the "chance" explanation becomes irrelevant

Question 40

When a difference is said to be "significant", it means that the difference probably

A) does not exist in the population
B) does exist in the population
C) is no longer related to the population
D) none of these

Question 41

A powerful test is one that is

A) less likely to commit the Type 2 error
B) more likely to commit the Type 2 error
C) more likely to accept the null hypothesis
D) less likely to detect a population difference

Question 42

If the tabled value for t, for a certain number of degrees of freedom, were 3.17, and the calculated value of t were 3.17, then

A) There is a failure to reject Ho
B) Ho is rejected
C) alpha becomes equal to zero
D) the t distribution must be normal

Question 43

The only time a difference between two sample means may be called "significant" is when

A) they are at least 10 points apart
B) they differ by at least .05 points
C) the first mean is larger than the second mean
D) the null hypothesis has been rejected

Question 44

The larger the effect size, the greater the likelihood

A) of ignoring the null hypothesis
B) of rejecting the null hypothesis
C) of committing the Type 2 error
D) that the population means are not significantly different

Question 45

Power can be defined as

A) One plus beta
B) Two plus beta
C) One minus beta
D) One minus alpha

Question 46

The alpha level sets the probability for the

A) Type 1 error
B) Type 2 error
C) Type 3 error
D) none of these

Question 47

The power of a statistical test, such as the independent t test, can be increased by

A) increasing the sample size
B) increasing the alpha error
C) using a one-tail test
D) all of these

Question 48

Every degree of freedom value specifies

A) a different t distribution
B) the same t distribution
C) that the t distribution must be assumed to be normal
D) the number of sample groups being compared

Question 49

The higher the likelihood of rejecting null when null really should be rejected, then

A) the higher becomes the value of beta
B) the less powerful the statistical test
C) the more powerful the statistical test
D) none of these, since rejecting the null hypothesis is not related to either

Question 50

The t distribution assumes normality only when

A) there are infinite degrees of freedom
B) there is a large degree of bias
C) the null hypothesis has been rejected
D) none of these, since the t distribution can never be normal

Question 51

The sign of the t ratio only becomes important to the statistical decision when

A) null is accepted
B) the degrees of freedom are infinite
C) alpha is set at .05 or less
D) calculating a one-tail t test

Question 52

According to the text, the value beyond which alpha should not be set, is

A) .01
B) .05
C) .50
D) 1.00

Question 53

To do a one-tail t test, as opposed to a two-tail,

A) the direction of the difference must always be specified beforehand
B) the direction of the difference need only be specified after null has been rejected
C) the direction of the difference must only be specified when null is accepted
D) the direction of the difference becomes irrelevant

Question 54

The effect size is determined by how much difference there is between the

A) two types of error, Type 1 and Type 2
B) population means in units of population standard deviations
C) population mean and the sample variance
D) sample mean and the population variance

Question 55

With infinite sample sizes, t ratios of +1.96

A) include only the middle-most 68% of all t values
B) include only the middle-most 50% of all t values
C) include only the middle-most 5% of all t values
D) exclude only the most extreme 5% of all t values

Question 56

Whenever the alternative hypothesis is written as "mean 1 is greater than mean 2", then

A) a one-tail t test is allowed
B) only a two-tail t test is allowed
C) an independent t test is not allowed
D) sample sizes must be greater than 30

Question 57

If an independent t ratio is to be calculated for a two-group design, 20 subjects in each group, then the degrees of freedom equal

A) 1
B) .05
C) 40
D) 38

Question 58

The t distributions deviate from normality when

A) the null hypothesis is being tested
B) the alpha is less than .05
C) sample sizes become smaller
D) none of these, since the t distribution never deviates from normality

Question 59

Anytime the probability of beta is reduced, then

A) power increases
B) power decreases
C) the likelihood of rejecting null is minimized
D) the likelihood of obtaining a significant difference is minimized

Question 60

With one degree of freedom, a significant t ratio will occur

A) 1% of the time
B) 99% of the time
C) 68% of the time
D) none of these, since degrees of freedom reflect sample sizes not frequency

Question 61

The distribution of differences is a distribution of sample measures.

Question 62

When the Levene test results in a significant value, .05 or less, then the variances can be assumed to be equal.

Question 63

If the Levene test resulted in a significance level greater than .05, then homogeneity of variance can be assumed.

Question 64

The estimated standard error of difference may never assume a negative value.

Question 65

The larger the sample sizes, the greater the degrees of freedom.

Question 66

When all the possible sample pairs have been selected from a single population, the mean of the distribution of differences is expected to approximate zero.

Question 67

The greater the number of degrees of freedom for the t ratio, the less the likelihood of rejecting the null hypothesis.

Question 68

With an infinite number of degrees of freedom the t distribution assumes normality.

Question 69

The mean of the distribution of differences becomes zero only when all sample pairs represent different populations.

Question 70

The true standard error of difference is equal to the standard deviation of the entire sampling distribution of differences when all the sample pairs in the population have been measured.

Question 71

The estimated standard error of difference estimates the value of the population mean.

Question 72

When the direction of the difference between two sample means is not specified, we must use the two-tail t.

Question 73

When the null hypothesis is rejected, then the alternative hypothesis must be accepted.

Question 74

When the two sample means are equal, the t ratio will always lead to an accept of the null hypothesis.

Question 75

The central limit theorem suggests that the entire distribution of differences between pairs of successively drawn sample means will approximate normality.

Question 76

The t ratio may only be calculated when the data are in ordinal form.

Question 77

When there is a failure to reject Ho then one may assume that the two sample groups represent a common population.

Question 78

The assumption of homogeneity of variance can be tested using the Levine Test.

Question 79

The estimated standard error of difference is an estimate of the variability occurring within the entire distribution of differences.

Question 80

Student's t test for two independent samples assumes that the variances within each of the two groups are NOT significantly different from each other.