Deck 8: Is There Really a Difference Introduction to Statistical Hypothesis Testing

Question 1

Which of the following z values is least likely to occur by chance?

A)z = +0.50
B)z = -1.00
C)z = -1.50
D)z = +2.00

Answer 1

D

Question 2

Nonparametric statistical tests often are called tests.

A)distribution-free
B)variance-free
C)null-parameter
D)nondirectional

Answer 2

A

Question 3

A statement about a characteristic of a population is a hypothesis.

A)demographic
B)statistical
C)research
D)primary

Answer 3

B

Question 4

One characteristic of the two hypotheses formulated for a statistical test is that the hypotheses must.

A)be statements about the same sample
B)specify the sample value
C)be written as a sentence
D)include all possible values of the parameter in the population

Question 5

Which of the following could be an appropriate null hypothesis for a statistical test concerning the mean income of 17-year old males?

Question 6

The statistical symbol H0 is used to represent a(n) hypothesis.

A)null
B)alternative
C)research
D)true

Question 7

The test statistic z locates a sample mean on a distribution.

A)positively skewed
B)negatively skewed
C)standard normal
D)symmetrical and bimodal

Question 8

The statistical symbol α is known as.

A)gamma
B)delta
C)beta
D)alpha

Question 9

Statistical tests require both a(n) and a(n) hypothesis.

A)null; alternative
B)primary; secondary
C)empirical; theoretical
D)conceptual; testable

Question 10

By setting alpha equal to .05, a "statistically rare" event is defined as an event occurring only 5 or fewer times in occasions if the hypothesis is true.

A)1000; null
B)100; null
C)100; alternative
D)1000; alternative

Question 11

The probability level that establishes how improbable an observed value of z must be in order to reject the null hypothesis is known as the level.

A)rejection
B)significance
C)decision
D)critical

Question 12

The statistical symbol H1 represents a(n) hypothesis.

A)null
B)alternative
C)research
D)true

Question 13

For a parametric test a statistical hypothesis is a statement about.

A)a characteristic of a sample
B)the range of values in the population
C)measures of central tendency for a sample
D)a characteristic of a population

Question 14

The null hypothesis establishes a situation under which the theoretical distribution of the test statistic may be obtained.

A)normal
B)mean
C)sampling
D)population

Question 15

A parametric statistical test involves hypotheses about.

A)sample statistics such as the mean and standard deviation
B)measures of central tendency such as the mode and median
C)population values such as the mean and variance
D)sample measures of central tendency and variability

Question 16

A statement that tentatively is held to be true about a population is called a(n) hypothesis.

A)alternative
B)population
C)null
D)true

Question 17

The level is a probability value that provides the criterion for rejecting H0.

A)significance
B)rareness
C)confidence
D)hypothesis

Question 18

One characteristic of the two hypotheses formulated for a statistical test is that the hypotheses must.

A)be statements about the same sample
B)specify the sample value
C)be mutually exclusive
D)be written as a sentence

Question 19

A statement of what must be true if the null hypothesis is false is called a(n) hypothesis.

A)population
B)research
C)alternative
D)true

Question 20

Which of the following could be an appropriate alternative hypothesis for a statistical test concerning the mean income of 17-year old males?

Question 21

If zobs does not fall into a rejection region, then the.

A)alternative hypothesis is not accepted
B)alternative hypothesis is not rejected
C)null hypothesis is rejected
D)null hypothesis is not accepted

Question 22

In behavioral research, alpha is usually set at.

A).10
B).05 or .01
C).01 or .001
D).005

Question 23

The rejection region represents the values of a test statistic that have a probability alpha if is true.

A)greater than; H0
B)greater than; H1
C)equal to or less than; H0
D)equal to or less than; H1

Question 24

If the null hypothesis is not rejected with a .05 significance level, then we know that.

A)there is a statistically significant difference
B)the alpha level is greater than .05
C)a non-directional test was used
D)the observed value of the test statistic did not fall into the rejection region

Question 25

If zobs equals -3.08 and zcrit equals plus or minus 1.96, then the statistical decisions should be as follows: the null hypothesis and the alternative hypothesis.

A)reject; do not accept
B)reject; accept
C)fail to reject; do not accept
D)fail to reject; accept

Question 26

Suppose a non-directional z test was performed and the null hypothesis rejected with a significance level of .05. Which one of the following could have been the value of zobs in the statistical test?

A)-1.98
B)-1.68
C)-1.34
D)+1.68

Question 27

A statistical test that locates rejection regions at both ends of the sampling distribution is called a test.

A)one-tailed
B)two-tailed
C)unidirectional
D)directional

Question 28

When rejection regions are located at both ends of a sampling distribution, a statistical test is used.

A)parametric
B)directional
C)one-tailed
D)non-directional

Question 29

A statistically significant difference with the z test means that.

A)the population mean is larger than the hypothesized sample value
B)the alpha level was higher than expected by chance alone
C)the sample mean comes from a population with a mean different from the hypothesized population value
D)the alpha level was lower than expected by chance alone

Question 30

The one-sample t test is calculated by dividing the difference of the by the.

A)sample mean minus the population mean; standard deviation
B)sample mean minus the population mean; standard error
C)individual's score minus the sample mean; standard deviation
D)individual's score minus the sample mean; standard error

Question 31

If the results of a study were summarized in a research article as z = -3.08, p < .05, then you would know that the.

A)results were not statistically significant at the .05 level
B)null hypothesis was not accepted at the .95 level
C)alternative hypothesis was rejected at the .05 level
D)null hypothesis was rejected at the .05 level

Question 32

The formula for the one-sample t test is.

Question 33

If zobs equals -.50 and zcrit equals plus or minus 1.96, then a statistical decision is to.

A)reject the null hypothesis
B)fail to reject the null hypothesis
C)accept the alternative hypothesis
D)fail to reject the alternative hypothesis

Question 34

If zobs does not fall into a rejection region, then the.

A)alternative hypothesis is accepted
B)alternative hypothesis is not rejected
C)null hypothesis is rejected
D)null hypothesis is not rejected

Question 35

If zobs falls into a rejection region, then the hypothesis is.

A)null; accepted
B)alternative; rejected
C)null; not rejected
D)alternative; accepted

Question 36

If zobs falls into a rejection region, then the hypothesis is.

A)null; accepted
B)alternative; rejected
C)null; rejected
D)alternative; not rejected

Question 37

The boundaries of the rejection region or regions are specified by.

A)the critical value
B)alpha
C)rejection region values
D)boundary values

Question 38

A nonsignificant difference with the z test means that.

A)the population mean is larger than the hypothesized sample value
B)H0 was rejected and H1 accepted
C)H0 was not rejected and H1 was not accepted d H0 was rejected and H1 not accepted

Question 39

A statistically significant difference means that.

A)the population mean is larger than the hypothesized sample value
B)H0 was rejected and H1 accepted
C)H0 was not rejected and H1 was not accepted
D)the alpha level was lower than expected by chance alone

Question 40

A one-sample t test is used to test for the difference between a.

A)sample standard deviation and a sample variance
B)population mean and a population variance
C)sample mean and a sample variance
D)sample mean and a population mean

Question 41

In a nondirectional one-sample t test, the rejection region is located in of the sampling distribution of t.

A)the center
B)the left tail
C)the right tail
D)both tails

Question 42

A one-sample t test is used with a sample of 30 scores. The df for this t are.

A)31
B)29
C)30 d 28

Question 43

The denominator of the one-sample t test is calculated by dividing by.

Question 44

To enter a table of critical values of t, you must know.

A)df for tobs
B)tobs
C)the value of X − μ
D)the value of s

Question 45

Which of the following would be an appropriate alternative hypothesis for the one-sample t test of the hypothesis that the mean reaction time of a population of 45 year-old drivers is 0.653 seconds?

Question 46

Degrees of freedom for a statistic refers to the number of that are free to vary when calculating that statistic.

A)sample statistics
B)population parameters
C)scores in the sample
D)scores in the population

Question 47

The concept of degrees of freedom refers to the.

A)number of scores plus one used to calculate the sample standard deviation for the one-sample t test
B)number of scores minus one used to calculate the population standard deviation for a t test
C)variation in critical values of t with differences in sample size
D)number of scores that are free to vary when calculating a statistic

Question 48

Degrees of freedom are represented by the abbreviation.

A)df
B)fd
C)def
D)degfr

Question 49

Which of the following is true about the t?

A)The sampling distribution of t is independent of the df.
B)The sampling distribution of t for df = 10 is flatter and wider than the sampling distribution for df = 5.
C)The sampling distribution of t for df = 5 is flatter and wider than the sampling distribution for df = 10.
D)There is a single sampling distribution of t for all values of df.

Question 50

The shape of the sampling distribution of t is.

A)typically normally distributed
B)positively skewed
C)determined by the degrees of freedom
D)identical to the distribution of z when the sample size is 30 or more

Question 51

Which of the following would be an appropriate null hypothesis for the one-sample t test of the hypothesis that the mean reaction time of a population of 45 year-old drivers is 0.653 seconds?

Question 52

The degrees of freedom for the one-sample t test are found by.

A)N
B)N - 1
C)N + 1
D)N - 2

Question 53

In a directional one-sample t test, the rejection region is located in of the sampling distribution of t.

A)the left tail
B)the right tail
C)either the left tail or the right tail, but not both tails
D)both tails

Question 54

When calculating s, the df are given by.

A)N
B)N + 1
C)N - 1
D)N - 2

Question 55

The degrees of freedom determine the the sampling distribution of t.

A)mean of
B)range of values for
C)variance of
D)shape of

Question 56

The theoretical sampling distribution of t varies with the.

A)value of the sample mean
B)range of values in the sample
C)size of the sample
D)value of the sample variance

Question 57

If tobs does not fall into a rejection region, then the decision is to.

A)reject the null hypothesis
B)fail to reject the null hypothesis
C)accept the alternative hypothesis
D)decrease the value of alpha

Question 58

In general, the t distribution is than the normal distribution.

A)more symmetrical
B)more peaked and less wide
C)more negatively skewed
D)flatter and wider

Question 59

If tobs falls into a rejection region, then the decision is to.

A)reject the null hypothesis
B)fail to reject the null hypothesis
C)do not accept the alternative hypothesis
D)increase the value of alpha

Question 60

When H0 is true, expected values of t are distributed symmetrically around a value.

A)of zero
B)of 1.0
C)of either +1.0 or -1.0
D)that varies with degrees of freedom

Question 61

If H0 is true and it is not rejected, then has occurred.

A)a Type I error
B)a Type II error
C)either a Type I or a Type II error
D)a correct decision

Question 62

If the result of a statistical test is reported as p > .05, then it indicates that the investigator .

A)failed to reject H0
B)failed to reject H1
C)accepted H1
D)rejected H0

Question 63

Alpha is the probability of.

A)rejecting H0 when it is true
B)failing to reject H0 when it is false
C)accepting H1 when it is true
D)rejecting H1 when it is true

Question 64

Underlying the use of the one-sample t test is the assumption that the.

A)distribution of scores in the sample is symmetrical
B)population variance is equal to the sample variance
C)degrees of freedom are greater than 30
D)scores in the population are normally distributed

Question 65

If the result of a one-sample t test is reported as t(49) = 2.329, p < .05, then you know that.

A)the critical value of t was 2.329
B)the alpha level was less than .05
C)the sample size was 49
D)none of the above

Question 66

A nonsignificant difference is attributed to.

A)the effects of stratified sampling
B)an insufficiently low alpha value
C)sampling error
D)a standard error

Question 67

If the result of a one-sample t test is reported as p > .05, then you know that the.

A)null hypothesis was rejected
B)null hypothesis was not rejected
C)alternative hypothesis was accepted
D)probability of a Type II error was .05

Question 68

If the observed difference between the sample mean and the hypothesized population mean in a one-sample t test is nonsignificant, then.

A)the null hypothesis was rejected
B)the null hypothesis was not rejected
C)it implies that a Type I error was made
D)the probability that a Type II error was made is equal to .05

Question 69

A Type I error occurs if the null hypothesis is when it is.

A)rejected; true
B)not rejected; true
C)rejected; false
D)not rejected; false

Question 70

The use of the one-sample t test rests on the assumption that the sample.

A)is symmetrical
B)was randomly selected from the population
C)variance is known
D)standard deviation is known

Question 71

If the null hypothesis is not rejected in a one-sample t test, then the.

A)sample mean and the population mean differ significantly from each other
B)alpha level should be increased
C)observed difference between the sample mean and the population mean is attributed to sampling error
D)distributions of scores within both the sample and the population are normal

Question 72

If tobs falls into a rejection region, then which of the following is true?

A)The probability of obtaining the value of tobs under the null hypothesis is greater than the alpha value.
B)The alternative hypothesis is not accepted.
C)The null hypothesis is rejected.
D)The null hypothesis is not rejected.

Question 73

If the result of a statistical test is reported as p < .05, then it indicates that the investigator .

A)failed to reject H0
B)failed to reject H1
C)rejected H1
D)rejected H0

Question 74

If the alternative hypothesis is true and H0 is not rejected, then.

A)a Type I error has occurred
B)a Type II error has occurred
C)a correct decision has occurred
D)it is possible that both a Type I and Type II error have occurred

Question 75

If the results of a study using the one-sample t test were summarized t(14) = 3.218, p < .01, then you would know that the probability of tobs if H0 is true is and that the difference between X and μ is.

A)less than or equal to .01; nonsignificant
B)less than or equal to.01; statistically significant
C)greater than .01; nonsignificant
D)greater than .01; statistically significant

Question 76

If a(n) hypothesis is rejected when it was in fact true, then a error has occurred.

A)null; Type I
B)alternative; Type I
C)null; Type II
D)alternative; Type II

Question 77

If tobs does not fall into a rejection region, then which of the following is true?

A)The probability of obtaining the value of tobs under the null hypothesis is less than the alpha value.
B)The alternative hypothesis is accepted.
C)The null hypothesis is rejected.
D)The null hypothesis is not rejected.

Question 78

If the results of a study using the one-sample t test were summarized t(99) = 1.546, p > .05, then you would know that the sample size was and the null hypothesis was
)

A)99; rejected
B)99; not rejected
C)100; rejected
D)100; not rejected

Question 79

You make a Type II error when you.

A)reject H0 when it is true and H1 is false
B)accept H1 when it is true and H0 is false
C)fail to reject H0 when it is false and H1 is true
D)fail to reject H1 when it is false and H0 is true

Question 80

If a(n) hypothesis is not rejected when in fact it is true, then error has occurred.

A)null; no
B)null; a Type I
C)alternative; no
D)alternative; a Type II