Deck 10: Independent Groups T-Test

Question 1

What would the value of eta-squared be if and independent t-test yielded an observed t value of -1.73 and the number of subjects in the placebo group was 10 and the number of subjects in the treatment group was 10.

A).142
B).132
C).266
D)None of these

Answer 1

.142

Question 2

Before a researcher decides what statistical test,and if an independent t-test is correct he/ she must determine_____.

A)The number of independent variables manipulated
B)Scale of measurement of the dependent variable (quantitative vs.qualitative)
C)Within or between subject design
D)The number of subjects used
E)All of these are correct

Answer 2

The number of subjects used

Question 3

Dr.Johnson is studying the effects of aspirin on heart rate.He believes that aspirin will lower heart rate.He has 2 groups the treatment group receives 80mg of aspirin for a week (n=4)the control group received a placebo (n=4)and their heart rates are compared.Below is his data in which heart rate is beats per minute.He sets his alpha level at 0.05 and uses a directional test.
What is Dr.Johnson's critical t-value?

A)1.860
B)2.306
C)1.943
D)1.895

Answer 3

1.943

Question 4

The 95% confidence intervals are_____reported in APA results sections.

A)never
B)usually
C)sometimes
D)None of these

Question 5

Dr.Johnson is studying the effects of aspirin on heart rate.He believes that aspirin will lower heart rate.He has 2 groups the treatment group receives 80mg of aspirin for a week (n=4)the control group received a placebo (n=4)and their heart rates are compared.Below is his data in which heart rate is beats per minute.He sets his alpha level at 0.05 and uses a directional test.
What is the 95% confidence intervals for Dr.Johnson's study?

A)5.78 to 15.72
B)5.99 to 15.52
C)6.78 to 17.78
D)None of these

Question 6

Dr.Johnson is studying the effects of aspirin on heart rate.He believes that aspirin will lower heart rate.He has 2 groups the treatment group receives 80mg of aspirin for a week (n=4)the control group received a placebo (n=4)and their heart rates are compared.Below is his data in which heart rate is beats per minute.He sets his alpha level at 0.05 and uses a directional test.
Can you reject the null hypothesis and concluded that aspirin lowers heart rate?

A)Yes,since the calculated t is greater than the table t
B)No,since the calculated t is greater than the table t
C)more information is necessary
D)None of these

Question 7

JJ just used an Independent groups t-test to analyze his data for his Master's degree and found that the t-value or his calculated t was equal to 3.05 based on his degrees of freedom of 60.The table t was 1.671 and he set his alpha level at .05 directional.Can he reject the null hypothesis and conclude the groups are significantly different.

A)No,he cannot reject the null
B)Yes,he can reject the null
C)He needs to run another test to determine if he has a type II error
D)Both a & c

Question 8

In an APA results section and independent groups t-test is written as follows t(82)= 5.66,p<0.05.Based on this information were the groups significantly different?

A)yes,since p<0.05
B)no,since p should be less than 0.01 to be significant
C)there may be a type II error
D)there may not be enough subjects

Question 9

Dr.Johnson is studying the effects of aspirin on heart rate.He believes that aspirin will lower heart rate.He has 2 groups the treatment group receives 80mg of aspirin for a week (n=4)the control group received a placebo (n=4)and their heart rates are compared.Below is his data in which heart rate is beats per minute.He sets his alpha level at 0.05 and uses a directional test.
What is the strength of the relationship?

A).75
B).72
C).67
D)None of these

Question 10

A directional alternative hypothesis is written as_____.

A)H₀: ì₁ = ì₂.
B)H₁: ì₁ > ì₂
C)H₀: ì₁ = ì₂
D)H₁: ì₁
ì₂

Question 11

Dr.Osborn believes that taking calcium will improve bone density in women.She uses a between subjects design and gives the treatment group Calcium everyday and the placebo group a sugar pill.Her scientific or alternative hypothesis is_____.

A)non-directional
B)directional
C)should not be between subjects
D)None of these

Question 12

A non-directional alternative hypothesis is written as _____.

A)H₀: ì₁ = ì₂.
B)H₁: ì₁ > ì₂
C)H₀: ì₁ = ì₂
D)H₁: ì₁
ì₂

Question 13

The Independent groups t-test assumes all of the following except_____.

A)homogeneity of variance
B)between subjects design
C)the dependent variable is ordinal
D)the population is normally distributed

Question 14

Dr.Johnson is studying the effects of aspirin on heart rate.He believes that aspirin will lower heart rate.He has 2 groups the treatment group receives 80mg of aspirin for a week (n=4)the control group received a placebo (n=4)and their heart rates are compared.Below is his data in which heart rate is beats per minute.He sets his alpha level at 0.05 and uses a directional test.
What is the t-value for the data above?

A)4.20
B)4.19
C)3.91
D)None of these

Question 15

The nature of the relationship is determined by_____

A)examining the sample means
B)examining the t-value
C)examining the confidence intervals
D)All of these

Question 16

An independent groups t-test has _____levels of the independent variable.

A)2 levels
B)3 levels
C)1 level
D)None of these

Question 17

The amount of sampling error is determined by_____.

A)Standard error of the difference
B)Standard error of the mean
C)Standard scores or z-scores
D)None of these

Question 18

In an APA results section and independent groups t-test is written as follows t(82)= 5.66,p<0.05.Based on this information what are the degrees of freedom?

A)5.66
B)82
C)80
D)cannot be determined

Question 19

Dr.Johnson is studying the effects of aspirin on heart rate.He believes that aspirin will lower heart rate.He has 2 groups the treatment group receives 80mg of aspirin for a week (n=4)the control group received a placebo (n=4)and their heart rates are compared.Below is his data in which heart rate is beats per minute.He sets his alpha level at 0.05 and uses a directional test.
Is it possible that Dr.Johnson has_____.

A)Type I error
B)sampling error
C)Type II error
D)Both a & b
E)All of these

Question 20

Confidence intervals are used to_____.

A)provide information about sampling error
B)whether of nor a relationship exist between the independent and dependent variables
C)whether or not homogeneity of variance has been violated.
D)Both a & b
E)All of these

Question 21

If the sample sizes are not equal,then the pooled variance estimate should be calculated ____.

A)using the unweighted mean of the variances
B)using a weighted mean of the variances
C)by reducing the size of one group to equal the size of the other group

Question 22

According to the homogeneity of variance assumption:

A)ó₁² + ó₂² = ó²
B)ó₁² = ó₂² = ó²
C)ó₁² - ó₂² = ó²
D)ó₁² = ó₂² + ó²

Question 23

The standard error of the difference becomes smaller as sample sizes _____ and the variability of the populations_____.

A)increase;increases
B)increase;decreases
C)decrease;decreases
D)decrease;increases

Question 24

Which of the following conditions would make it inappropriate to use an independent-groups t test?

A)when the independent variable is qualitative
B)when the independent variable is within-subjects
C)when the independent variable is quantitative
D)when the dependent variable is measured on a level that approximates interval characteristics

Question 25

By pooling the variance estimates from the two populations,we increase the _____ on which the estimate of ó² is based and thereby obtain a better estimate.

A)degrees of freedom
B)power
C)population size
D)standard error

Question 26

The mean of the sampling distribution of the difference between two independent means is _____ to the difference between the population means for the groups in question.

A)always equal
B)sometimes equal
C)never equal
D)none of these

Question 27

The standard deviation of the sampling distribution of the difference between two independent means is called the:

A)standard error of the mean
B)standard difference of error
C)standard error of the difference between independent means
D)none of these

Question 28

The procedure which produces a pooled weighted estimate of the sample variances combines the individual estimates in a manner which is ____.

A)proportional to their mean difference
B)unaffected by sample size
C)proportional to their degrees of freedom
D)proportional to the size of difference between the variance estimates

Question 29

The standard error of the difference becomes smaller as the sample sizes _____ and the variability of the scores in the populations _____.

A)decrease;increases
B)decrease;decreases
C)increase;decreases
D)increase;increases

Question 30

In practice,we typically know the values of _____,but we do not know the values of _____.

A)n₁ and n₂;ó₁² and ó₂²
B)the sample means;n₁ and n₂
C)n₁ and n₂;the sample means
D)ó₁² and ó₂²;n₁ and n₂

Question 31

The independent groups t test is typically used to analyze the relationship between two variables when:

A)the independent variable is quantitative in nature and is measured on a level that at least approximates interval characteristics
B)the independent variable is between-subjects in nature
C)the independent variable has two and only two levels
D)all of these

Question 32

When the independent variable has more than two levels which of the following statistical techniques may be used to investigate the relationship between the independent and dependent variables?

A)a one-sample t test
B)a one sample z test
C)an independent-groups t test
D)none of these

Question 33

The mean of a sampling distribution of the difference between two independent means is always equal to the:

A)difference between the population means
B)difference between the sample means
C)standard error of estimate
D)standard error of the difference

Question 34

The null hypothesis for an independent groups t test states that _____.

A)the population mean scores for each level of the independent variable are the same
B)the two groups have different population means on the dependent variable
C)the independent and dependent variables are related
D)the population variances are the same

Question 35

Independent-groups t tests may be used to analyze the relationship between two variables when _____.

A)the dependent variable is quantitative
B)the independent variable is between-subjects in nature
C)the independent variable has only two levels
D)all of these

Question 36

If the variability of scores in the populations is held constant,then increasing sample sizes results in _____ in the standard error of the difference.

A)no change
B)a decrease
C)an increase
D)all of these apply

Question 37

The standard error of the difference indicates how much _____ will occur,on the average.

A)sampling error
B)error variance
C)population error
D)differential error

Question 38

The standard error of the difference between two independent means is influenced by _____.

A)the sample size of both groups
B)population variance of both groups
C)both a and b
D)none of these

Question 39

The size of the standard error of the difference is influenced by:

A)the sample sizes
B)the variability of scores in the population
C)neither a nor b
D)a and b

Question 40

The alternative hypothesis for an independent-groups t test states that _____.

A)the two levels of the independent variable are essentially the same
B)the independent and dependent variables are related
C)the independent and dependent variables are unrelated
D)the dependent variable influences the value of the independent variable

Question 41

Treatment effects are defined as the difference between a given _____ and the _____.

A)grand mean;population mean
B)sample mean;population mean
C)group mean;grand mean
D)raw score;group mean

Question 42

A formula used to calculate eta² is ____.

A)t ²t ² - 1
B)t ²/(t ² + df )
C)SS_EXPLAINED /SS_TOTAL
D)both b and c

Question 43

For the t test to be considered robust to violations of certain assumptions,the samples should be ____.

A)relatively large
B)approximately equal
C)both a and b
D)none of these

Question 44

The total variability in the dependent variable,as represented by SS_TOTAL,can be spilt up,or partitioned,into two components:

A)SS_EXPLAINED + SS_ERROR
B)SS_UNEXPLAINED + SS_ERROR
C)SS_EXPLAINED + SS_IV
D)none of these

Question 45

The _____ represents the total amount of _____ that exists in the data.

A)sum of squares total;error
B)sum of squares error;variability
C)sum of squares total;variability
D)none of these

Question 46

The set of all t values more extreme than the critical values constitutes a(n)_____ result or more formally,the _____ region.

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

Question 47

If the sample sizes in the two groups are each greater than _____ and roughly comparable,then the independent groups t test is robust to rather severe departures of the _____ assumption.

A)40;normality
B)100;heterogeneity of variance
C)40;probability
D)100;unequal n

Question 48

Typically,research in the behavioral sciences involves _____ values of eta-squared.

A)extremely large
B)somewhat large
C)moderate
D)relatively small

Question 49

Under certain conditions,the independent groups t test is robust to violations of the _____ and _____ assumptions.

A)equal n;heterogeneity of variance
B)randomization;independence
C)normality;homogeneity of variance
D)unequal n;normality

Question 50

Which of the following assumptions applies to the independent groups t test?

A)The samples have been randomly drawn from their respective populations.
B)The scores in each population are normally distributed.
C)The variances of both populations are homogeneous.
D)All of these

Question 51

_____ represents the proportion of variability in the dependent variable that is not associated with the independent variable--that is,the proportion of variability that is due to disturbance variables.

A)eta-squared
B)1.00 plus eta-squared
C)1.00 minus eta-squared
D)eta-squared minus 1.00

Question 52

What assumption is made so that the pooled variance estimate can be substituted for the population variances within the standard error of the differences formula?

A)the population variances are homogeneous.
B)the population variances are heterogeneous.
C)the sample sizes are equal.
D)the sample sizes are large.

Question 53

The measure of the strength of the relationship between the independent and dependent variables in the "cold/warm environment" data is ____.

A)2.667²/(2.667² + 16)
B)2.120²/(2.120² + 16)
C).05
D)2.667²/2.667 + 18

Question 54

Unexplained variance or error variance reflects the influence of:

A)treatment effects
B)confounding variables
C)control variables
D)disturbance variables

Question 55

Eta-squared indexes the _____ of the relationship between the independent and dependent variables since it represents the _____ of variability in the dependent variable that is associated with the independent variable.

A)direction;proportion
B)strength;proportion
C)nature;percentage
D)significance;percentage

Question 56

The independent groups t test is quite robust to the assumption of homogeneity of variance when the _____ are _____.

A)variances;unequal
B)sample sizes;equal
C)sample sizes;fairly discrepant
D)means;independent

Question 57

Which of the following indices measures the strength of the relationship between the independent and dependent variables?

A)standard error of difference
B)power
C)eta²
D)alpha

Question 58

The t statistic follows a t distribution when:

A)the samples are independently and randomly selected from their respective populations
B)the scores in each population are normally distributed
C)the scores in the two populations have equal variances
D)all of these

Question 59

The degrees of freedom for the independent groups t test are equal to:

A)n₁ - n₂ + 2
B)n₁ + n₂ - 2
C)n₁ - n₂ - 2
D)n₁ + n₂ + 2

Question 60

If the observed t value exceeds the critical t value,then the difference between the sample means is most likely ____.

A)attributable to sampling error
B)nonsignificant
C)not attributable to sampling error
D)not very reliable

Question 61

The mean of a sampling distribution of the differences between two independent means

A)always equals zero
B)always equals one
C)always equals the difference between the sample means
D)always equals the difference between the population means

Question 62

The power of a statistical test is influenced by ____.

A)the strength of the relationship between the two variables in population
B)the sample sizes
C)the alpha level
D)all of these

Question 63

If the 95% confidence interval of a mean difference is -1 to 3,then the null hypothesis in the analysis was rejected.

Question 64

A physical therapist is interested in whether people with different bone structures will be affected differently by her new therapy program.She randomly chooses two groups of patients based on bone type: small-boned frame (X_S)and large-boned frame (X_L).Patients all had similar injuries.She measures the number of days each person takes to progress to a predetermined point.Here is the data:
What is the estimated standard error of the difference?

A)1.13
B)1.28
C)1.63
D)3.30

Question 65

When researchers fail to present the value of eta squared in a manuscript,this information can still be derived by the reader based on the observed t value and the degrees of freedom.

Question 66

Which of the following is NOT one of the steps of hypothesis testing used when comparing two independent means?

A)Assuming the null is true,state an expected result in the form of a range of values within which the difference between sample means is expected to fall
B)Assuming the alternative is true,characterize the mean and standard deviation of the sampling distribution of the differences between two independent means
C)Convert the observed difference between sample means into a t value
D)Translate the research question into a null and an alternative hypothesis

Question 67

A physical therapist is interested in whether people with different bone structures will be affected differently by her new therapy program.She randomly chooses two groups of patients based on bone type: small-boned frame (X_S)and large-boned frame (X_L).Patients all had similar injuries.She measures the number of days each person takes to progress to a predetermined point.Here is the data:
What is the pooled variance estimate?

A)0.70
B)1.13
C)2.13
D)4.54

Question 68

The Levene test

A)evaluates the null hypothesis of equal means in the populations against an alternative hypothesis of unequal means in the populations
B)evaluates the null hypothesis of unequal means in the populations against an alternative hypothesis of equal means in the populations
C)evaluates the null hypothesis of equal variances in the populations against an alternative hypothesis of unequal variances in the populations
D)evaluates the null hypothesis of unequal variances in the populations against an alternative hypothesis of equal variances in the populations

Question 69

A physical therapist is interested in whether people with different bone structures will be affected differently by her new therapy program.She randomly chooses two groups of patients based on bone type: small-boned frame (X_S)and large-boned frame (X_L).Patients all had similar injuries.She measures the number of days each person takes to progress to a predetermined point.Here is the data:
What is the null hypothesis?

A)µ_S = µ_L
B)µ_S
µ_L
C)µ_S < µ_L
D)µ_S > µ_L

Question 70

The nature of the relationship in the independent groups t test is determined by examining:

A)eta-squared
B)omega-squared
C)sample means
D)population means

Question 71

Suppose a researcher is reporting the results of an independent groups t test.If he obtained a statistically significant t value of 2.5 with 15 subjects in each group using an alpha level of .05,how would he report this in a psychological journal?

A)t (14)= 2.5,p < .05
B)t (14)= 2.5,p > .05
C)t (28)= 2.5,p < .05
D)t (29)= 2.5,p < .05

Question 72

A physical therapist is interested in whether people with different bone structures will be affected differently by her new therapy program.She randomly chooses two groups of patients based on bone type: small-boned frame (X_S)and large-boned frame (X_L).Patients all had similar injuries.She measures the number of days each person takes to progress to a predetermined point.Here is the data:
What are the degrees of freedom for the t test for two independent samples?

A)3
B)25
C)26
D)27

Question 73

A physical therapist is interested in whether people with different bone structures will be affected differently by her new therapy program.She randomly chooses two groups of patients based on bone type: small-boned frame (X_S)and large-boned frame (X_L).Patients all had similar injuries.She measures the number of days each person takes to progress to a predetermined point.Here is the data:
What is the observed value of the independent groups t test?

A)-0.61
B)-1.23
C)-1.56
D)-1.77

Question 74

What is an estimated pooled variance?

A)the weighted average of the variances estimates
B)the variance of the difference between the sample means
C)the sum of the two variances estimates
D)the variance of the populations from which the samples were drawn

Question 75

Eta-squared is a(n)_____ estimator in that it tends to slightly _____ the strength of the relationship in the population across random samples.

A)unbiased;overestimate
B)biased;underestimate
C)unbiased;underestimate
D)biased;overestimate

Question 76

A physical therapist is interested in whether people with different bone structures will be affected differently by her new therapy program.She randomly chooses two groups of patients based on bone type: small-boned frame (X_S)and large-boned frame (X_L).Patients all had similar injuries.She measures the number of days each person takes to progress to a predetermined point.Here is the data:
What are the critical values of t if the alpha level is .05?

A) $\pm$ 1.708
B) $\pm$ 2.052
C) $\pm$ 2.056
D) $\pm$ 2.060

Question 77

As the alpha level becomes larger,the power of a statistical test ____.

A)will decrease
B)will increase
C)remains the same
D)may decrease

Question 78

If a mean difference is 5,the estimated standard error of a mean difference is 4 and the nondirectional critical value of t for an alpha level of 0.05 is 2,what is the 95% confidence interval for the mean difference

A)1 to 9
B)3 to 7
C)-3 to 13
D)-1 to 11

Question 79

When sample sizes are small,power will tend to be __,everything else being equal.

A)low
B)moderate
C)high
D)there is no affect

Question 80

The calculation of eta-squared _____ when the statistical test is nonsignificant.

A)can be useful
B)is not necessary
C)is misleading
D)is not possible