Deck 8: Hypothesis Testing: Inferences About a Single Mean

Question 1

If the observed result of an investigation is so discrepant from the expected result that the difference cannot be attributed to chance,then the _____ hypothesis is _____.

A)alternative;rejected
B)null;rejected
C)alternative;accepted
D)null;accepted

Answer 1

null;rejected

Question 2

A sampling distribution of means based on all possible random samples of N=25,drawn from a population having a µ of 25 and a ó of 4,will have a mean of _____ and standard deviation of _____.

A)25;4
B)25;.8
C)25;.16
D)unknown;.8

Answer 2

25;.8

Question 3

As part of the process of hypothesis testing,the task of a researcher is to choose between _____.

A)N or n
B)Z or µ
C)H₀ and H₁
D)µ or ó

Answer 3

H₀ and H₁

Question 4

The fourth step in the one sample z test is the conversion of the observed sample mean into a z value to determine how many _____ it is away from _____,assuming the null hypothesis is true.

A)standard scores;ó
B)standard errors;ì
C)standard deviations;z

Question 5

The set of all standard scores that are more extreme than the critical values (that is,less than the negative critical value or greater than the positive critical value.is called a(n)_____ region and constitutes a(n)_____ result.

A)acceptance;unexpected
B)acceptance;expected
C)rejection;expected
D)rejection;unexpected

Question 6

A probability value that defines a region associated with unexpected results is known as _____.

A)alpha
B)beta
C)gamma
D)1-alpha

Question 7

The statement "to fail to reject the null hypothesis" would be made when the observed value of z ______.

A)falls within the region bounded by the critical values
B)falls beyond the critical values
C)could have occurred by chance less than .05
D)is -2.00

Question 8

If the observed and expected results of some experiment are not identical,then the null hypothesis (no differences)should be ______.

A)rejected
B)rejected only if the discrepancy cannot be attributed to chance
C)accepted
D)accepted only if experiment is repeated

Question 9

A sampling distribution of means based on all possible random samples of size 25,drawn from a population with a mean of 100,will have a standard error of _____.

A)5
B)4
C)20
D)can't determine above

Question 10

The formula for determining the standard error of the population mean is _____.

A)ó/
B)ó/N
C)ó/N-1
D)s/N-1

Question 11

When the alpha level is .05,a result is defined as being "unexpected" if the probability of obtaining that result,assuming the null hypothesis is true,is:

A)less than .95
B)greater than .95
C)less than .05
D)greater than .05

Question 12

Rejection regions are determined with reference to a probability value known as a(n):

A)alpha level
B)beta level
C)probability level
D)z level

Question 13

The most likely conclusion to make if your observed z exceeds the critical value is the _____.

A)null hypothesis is true
B)the population mean is equal to the value specified in the null hypothesis
C)the sample mean is different from the population mean
D)the population mean is different from the value specified in the null hypothesis

Question 14

If you conducted an experiment and observed results that indicated a very large discrepancy between the observed and expected results,then you probably would ______.

A)accept the null hypothesis of "no difference"
B)repeat the experiment until expected results are obtained
C)reject the null hypothesis
D)repeat the experiment until no discrepancies are observed

Question 15

In the process of hypothesis testing,the investigator begins by stating a proposal,or hypothesis,that is assumed to be:

Question 16

The formula that we use to test the hypothesis that a simple mean was drawn from a population with µ=100 and ó=9 is _____.

A)z=(
-ì)/N
B)z=(
- ì)/ ó

C)z=(
-ì)/

D)none of these

Question 17

If a researcher sets a critical z value equal to $\pm$ 1.96,then test statistics falling beyond that range _____.

A)suggest the null hypothesis is true
B)suggest that the alternative hypothesis is false
C)indicate an error has been made
D)suggest that the alternative hypothesis is true

Question 18

Which of the following describes a typical null hypothesis?

A)µ=150
B)µ
150
C)µ<150
D)µ>150

Question 19

Informally,the _____ hypothesis can be thought of as the hypothesis of _____.

A)alternative;minimal difference
B)null;significant difference
C)null;no difference
D)alternative;mean difference

Question 20

Traditionally,_____ is the probability associated with alpha.

A).05
B).025
C).50
D)1-.05

Question 21

Rejection of the null hypothesis when it is true is called a:

A)Type I error
B)Type II error
C)Type III error
D)none of these

Question 22

The alpha level directly affects the power of the statistical test,with more _____ alpha levels yielding _____ tests,everything else being equal.

A)conservative;more powerful
B)liberal;less powerful
C)conservative;less powerful
D)none of these

Question 23

The probability of making a Type I error is equal to:

A)the alpha level
B).05,in most cases
C)á
D)all of these

Question 24

The _____ the sample size,the _____ the statistical test will be,everything else being equal.

A)smaller;more powerful
B)smaller;less powerful
C)larger;more powerful
D)b and c

Question 25

The probability of making a _____ error is traditionally called beta.

A)sampling
B)Type I
C)Type II
D)rejection

Question 26

When the observed value of z falls within the range defined by the critical values,we _____ the null hypothesis.

A)fail to reject
B)fail to accept
C)reject
D)accept

Question 27

If you fail to reject the H₀ when H₀ is false then you made a _____ with a probability equal to ______.

A)Type I error;á
B)Type II error;â
C)Type I error;â
D)Type II error,á

Question 28

The probability for Type I error is equal to _____.

A).05
B)â
C)á
D)1-á

Question 29

Type II errors have a probability of occurring equal to _____.

A)â
B)1-â
C)1-á
D)á

Question 30

The probability that an investigator will correctly reject the null hypothesis when it is false is called the _____ of the statistical test.

A)beta
B)power
C)alpha
D)p value

Question 31

Type I errors occur when we ______.

A)reject a null hypothesis that is true
B)accept a null hypothesis that is false
C)fail to reject a null hypothesis that is false
D)accept an alternative hypothesis only 95% of the time.

Question 32

The probability,given a true null hypothesis,of not making a Type I error--that is,of failing to reject a false null hypothesis--is defined by:

A)1 - á
B)1 - â
C)1 - .95
D)1 - z

Question 33

When a researcher obtains a result that is consistent with the null hypothesis,he or she _____ the null hypothesis.

A)rejects
B)accepts
C)fails to accept
D)fails to reject

Question 34

Failure to reject the null hypothesis when it is false is called a:

A)Type I error
B)Type II error
C)Type III error
D)none of these

Question 35

Type II errors are made when you _____ H₀ and H₀ is _____.

A)reject;false
B)fail to reject;false
C)accept;true
D)fail to reject;true

Question 36

In principle,we can _____ accept the null hypothesis as being _____ via our statistical methods.

A)sometimes;true
B)never;false
C)always;true
D)never;true

Question 37

As a rough guide,investigators generally attempt to achieve statistical power (the probability of correctly rejecting the null hypothesis when it is false.in the range of _____ to _____.

A)á to â
B)0 to 1.0
C).05 to .95
D).80 to .95

Question 38

If a researcher rejects a null hypothesis that is true,then a _____ has been made.

A)Type II error
B)sampling error
C)Type I error
D)correct decision

Question 39

For an alpha level of .05,an unexpected result in the one sample z test includes any sample mean occurring more than _____ standard errors below or more than _____ standard errors above the value of ì represented in the null hypothesis.

A).95
B)1.96
C).05
D)1.0

Question 40

To avoid making a Type I error,we should use _____ level.

A)a liberal â
B)a conservative á
C)a smaller N
D)a liberal á

Question 41

The power of a statistical test can be increased by _____.

A)increasing á level
B)increasing sample size
C)all of these

Question 42

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section.The population standard deviation of the SAT is known to be 100.Use an alpha level of .05 when answering the following questions.What should be the critical value?

A)-1.96 and +1.96
B)-1.645
C)+1.645
D)+1.96

Question 43

Based on the Method of Presentation section of Chapter 8,suppose you obtained a statistically significant t value of 2.5 with 15 subjects using an alpha level of .05.How would this be reported in a psychological journal?

A)t (15)= 2.5,p < .05
B)t (15)= 2.5,p > .05
C)t (14)= 2.5,p < .05
D)t (14)= 2.5,p > .05

Question 44

The terms "statistically significant" and "statistically nonsignificant" are meant to apply:

A)only to the statistical outcome
B)only to the practical implications
C)only to Type II outcomes
D)only to real-world outcomes

Question 45

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section.The population standard deviation of the SAT is known to be 100.Use an alpha level of .05 when answering the following questions.What is the alternative hypothesis?

A)H₁: ì
500
B)H₁: ì < 500
C)H₁: ì > 500
D)H₁: ì = 500

Question 46

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section.The population standard deviation of the SAT is known to be 100.Use an alpha level of .05 when answering the following questions.What is the null hypothesis?

A)H₀: ì
500
B)H₀: ì < 500
C)H₀: ì > 500
D)H₀: ì = 500

Question 47

In general,a directional test will be _____ than a corresponding nondirectional test if the actual population mean and the hypothesized population mean differ in the specified direction.

A)less accurate
B)less powerful
C)more practical
D)more powerful

Question 48

In the Applications to the Analysis of Social Problems section of Chapter 8,the confidence intervals for the mean age at which mothers think parents should talk with children about sex and the confidence intervals for the mean age at which mothers think parents should talk with children about birth control were relatively narrow.What does this mean?

A)there is not a high level of confidence in these means
B)the means for these two variables lie in the rejection region
C)there are small amounts of sampling error
D)none of these

Question 49

Directional tests are often referred to as :

A)unbiased tests
B)single distribution tests
C)one-sample tests
D)one-tailed tests

Question 50

An alternative hypothesis that specifies that a population mean is different from a given value and also indicates the direction of that difference is called a:

A)differential alternative hypothesis
B)directional alternative hypothesis
C)a and b
D)neither a nor b

Question 51

The one-sample t test is based on the assumption that:

A)the sample is independently and randomly selected from the population of interest
B)the scores on the variable are normally distributed
C)the variable being studied is qualitative in nature
D)a and b

Question 52

Based on the Method of Presentation section of Chapter 8,the null and alternative hypotheses should be formally written out when reporting the results of a statistical test in a psychological journal.

Question 53

A t value is analogous to a z score except that it represents the number of _____ a sample mean is from ì.

A)standard errors
B)standard deviations
C)estimated standard errors
D)estimated standard deviations

Question 54

Which characteristics of the t distribution influences its shape?

A)population mean
B)sample size
C)sample mean
D)size of confidence interval

Question 55

When _____,and the raw scores in the population are normally distributed,then the normal and t distributions are quite _____ one another.

A)N < 40;similar to
B)N > 40;similar to
C)N = 40;different from
D)none of these

Question 56

When we say that a test is _____ to violations of a distributional assumption,we mean that the frequency of Type I and Type II errors,and,thus,the accuracy of our conclusions,are relatively unaffected as compared to when the assumption is met.

A)vulnerable
B)sensitive
C)immune
D)robust

Question 57

In hypothesis testing,which of the following is assumed to be true?

A)alternative hypothesis
B)null hypothesis
C)competing hypothesis
D)cannot be determined

Question 58

When there is exclusive concern that the population mean differs from a value in a specified direction,we should use _____.

A)a nondirectional test
B)a directional test
C)a stringent á
D)both a and c above

Question 59

Which of the following statements is an example of a two-tailed alternative hypothesis?

A)H₁:µ₁>µ₂
B)H₁:µ₁= µ₂
C)H₁:µ₂>µ₁
D)H₁:µ₁

µ₂

Question 60

The critical t value needed to reject the null will always be _____ than a Z value for the same set of scores.

A)less
B)larger
C)equal
D)different

Question 61

Which of the following accurately defines a Type II error?

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

Question 62

A one-sample t test is used in situations where

A)the s is known.
B)the s must be estimated from a sample.
C)the alternative hypothesis is directional only.
D)the alternative hypothesis is nondirectional only.

Question 63

A statistically significant result will always have important practical implications.

Question 64

The one-sample z test is used to determine whether the difference between your sample mean and the hypothesized population value is _____.

A)due to sampling error
B)significantly large in the "real world"
C)due to mistakes made when collecting data
D)both a and b

Question 65

In a one-sample z-test,the term "statistically significant difference" tells you _____.

A)your sample mean differs from the hypothesized value by more than would be expected from sampling error alone
B)the difference between your sample mean and the hypothesized value is large and meaningful in the "real world"
C)there is a non-zero correlation coefficient between your independent and dependent variables
D)all of these

Question 66

If N = 30,the sample mean is 12,and the estimated standard error of the mean is 2,what are the 95% confidence intervals?

A)7.91 to 16.09
B)7.916 to 16.084
C)8.08 to 15.92
D)8.602 to 15.398

Question 67

When we use inferential statistics to address a research question,we _____.

A)have collected information from the entire population
B)perform all calculations in the same way as with descriptive statistics
C)make generalizations from a sample to the population it was sampled from
D)all of these

Question 68

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section.The population standard deviation of the SAT is known to be 100.Use an alpha level of .05 when answering the following questions.What conclusions can be made,based on this test statistic?

A)The score of the students who took the Kaplan course was better than the national mean only because of sampling error.
B)The Kaplan course helped the students score statistically significantly higher than the national mean.
C)The Kaplan course helped the students score statistically significantly lower than the national mean.
D)none of these conclusions can be made

Question 69

Which of the following is NOT one of the conditions for using the one-sample z test?

A)The variable under investigation is quantitative.
B)The variable under investigation at least approximates interval level characteristics.
C)The variable under investigation is qualitative and measured on an ordinal level.
D)The researcher knows the population standard deviation.

Question 70

Which of the following symbols represents the power of a statistical test?

A)a
B)b
C)1 - a
D)1 - b

Question 71

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section.The population standard deviation of the SAT is known to be 100.Use an alpha level of .05 when answering the following questions.The students who took the Kaplan course obtain a mean of 520 on the math SAT.Compute the one-sample z test statistic.

A)z = 2.83
B)z = 1.41
C)z = .014
D)z = .20

Question 72

The one-sample t-test is robust to violations against which of the following assumptions?

A)the sample is independently selected from the population of interest
B)the sample is randomly selected from the population of interest
C)scores on the variables are normally distributed in the population
D)the variable being studied is qualitative in nature

Question 73

Which of the following alternative hypotheses would require using a one-tailed test?

A)H₁: ì
100
B)H₁: ì < 100
C)H₁: ì > 100
D)H₁: ì = 100
E)either b or c

Question 74

A confidence claim reflects a _____ of an extended number of confidence intervals across all possible random samples of a given size.

A)short-term performance
B)long-term performance
C)zero-sum performance
D)proportional performance

Question 75

Which of the following accurately defines a Type I error?

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

Question 76

The _____ is a probability value determined by the experimenter to define the _____,which is the set of all scores more extreme than the critical values.

A)alpha level;rejection region
B)rejection region;alpha level
C)critical value;rejection region
D)beta level;alpha level

Question 77

What happens when the experimental results are statistically significant?

A)The alternative hypothesis is proven.
B)The alternative hypothesis is rejected.
C)The null hypothesis is rejected.
D)The null hypothesis is accepteD.

Question 78

Why would a researcher want high statistical power rather than low statistical power?

A)the chances of making a Type I error would be less
B)the chances of making a Type II error would be less
C)the chances of making a Type I error would be greater
D)the chances of making a Type II error would be greater

Question 79

Which of the following statements is NOT true?

A)as a increases,b decreases
B)as N increases,power increases
C)as b increases,power increases
D)as a increases,power increases

Question 80

The values that define the boundaries of the _____ are called the _____.

A)confidence interval;confidence limits
B)confidence limits;confidence intervals
C)confidence interval;alphas
D)none of these