Psyk500 study guide  Mathematics homework help
Question 1
 What proportion of a normal distribution is located in the tail below z = 2.00?

a. 
0.9772 
[removed] 
b. 
0.4772 
c. 
0.0228 

d. 
0.0456 
Question 2
 In analysis of variance, each independent variable is referred to as a ____.

a. 
stage 
[removed] 
b. 
comparison 

c. 
factor 
[removed] 
d. 
level 
Question 3
 Which outcome is expected if the null hypothesis is true for an analysis of variance?

a. 
SS_{between} should be about the same size as SS_{within}. 

b. 
MS_{between} should be about the same size as MS_{within}. 
[removed] 
c. 
SS_{between} should be about the same size as SS_{total}. 
[removed] 
d. 
MS_{between} should be about the same size as MS_{total}. 
Question 4
 A researcher measures IQ and weight for a group of college students. What kind of correlation is likely to be obtained for these two variables?

a. 
a correlation near one 

b. 
a positive correlation 

c. 
a correlation near zero 
[removed] 
d. 
a negative correlation 
Question 5
 A sample of difference scores has a mean of M_{D} = 5 with a variance of s^{2} = 100. If effect size is measured using Cohen’s d, what is the value of d?

a. 
This cannot be determined without knowing the sample size. 

b. 
d = 25/100 

c. 
d = 5/100 

d. 
d = 5/10 
Question 6
 What is the value of the median for the following set of scores? Scores: 1, 3, 4, 6, 7, 8, 12, 23

a. 
6.5 

b. 
8 

c. 
6 

d. 
7 
Question 7
 The following X and Y scores produce SS_{X} = 2 and SP = 8. What is the regression equation for predicting Y?
X Y
1 2
2 3
3 10

a. 
Y = 0.25X + 4.5 

b. 
Y = 0.25X – 4.5 

c. 
Y = 4X – 3 
[removed] 
d. 
Y = 4X + 3 
Question 8
 For a repeatedmeasures study comparing three treatment conditions with a sample of n = 4 participants, what are the degrees of freedom for the repeatedmeasures Fratio?
[removed] 
a. 
2, 11 

b. 
2, 6 

c. 
2, 9 
[removed] 
d. 
3, 11 
Question 9
 What is the value of Σ(X – 2 )^{2} for the following scores? Scores: 2, 3, 5

a. 
36 

b. 
10 
[removed] 
c. 
16 
[removed] 
d. 
8 
If sample variance is computed by dividing SS by df = n – 1, then the average value of the sample variances from all the possible random samples will be ____ the population variance.

a. 
unrelated to 

b. 
exactly equal to 

c. 
smaller than 
[removed] 
d. 
larger than 
Question 11
 The percentage of variance accounted for by the treatment effect is usually known as _____ in published reports of ANOVA results.

a. 
η^{2} 

b. 
α^{2} 

c. 
σ^{2} 

d. 
µ^{2} 
Question 12
 In general, what factors are most likely to reject the null hypothesis for an ANOVA?

a. 
large mean differences and small variances 

b. 
small mean differences and large variances 

c. 
large mean differences and large variances 

d. 
small mean differences and small variances 
Question 13
 In a twofactor experiment with two levels of factor A and two levels of factor B, three of the treatment means are essentially identical and one is substantially different from the others. What result(s) would be produced by this pattern of treatment means?
[removed] 
a. 
a main effect for factor B 
[removed] 
b. 
a main effect for factor A 
[removed] 
c. 
main effects for both A and B, and an interaction 
[removed] 
d. 
an interaction between A and B 
Question 14
 A repeatedmeasures ANOVA has SS_{within treatments} = 26 and SS_{between subjects} = 12. For this analysis, what is the value for SS_{error}?
Question 15
 For a population with a standard deviation of σ = 6, what is the zscore corresponding to a score that is 12 points above the mean?

a. 
z = 2 

b. 
z = 1 

c. 
z = 6 

d. 
z = 12 
Question 16
 A sample consists of n = 16 scores. How many of the scores are used to calculate the range?
Question 17
 A multiplechoice test with 48 questions has four choices for each question. What is the probability of getting more than 12 questions correct by just guessing?

a. 
0.0675 

b. 
0.4325 

c. 
0.5000 

d. 
0.5675 
Question 18
 A hypothesis test produces a t statistic of t = 2.20. If the researcher is using a twotailed test with α = .05, how large does the sample have to be in order to reject the null hypothesis?

a. 
At least n = 14 

b. 
At least n = 12 

c. 
At least n = 13 
[removed] 
d. 
At least n = 11 
uestion 19
 For a linear regression calculated for a sample of n = 20 pairs of X and Y values, what is the value for degrees of freedom for the predicted portion of the Yscore variance, MS_{regression}?

a. 
19 

b. 
18 

c. 
1 
[removed] 
d. 
2 
Question 20
 A population has a mean of µ = 30. If 3 points are added to each score, what is the mean for the new distribution?
Question 21
 What is the median for the following set of scores? Scores: 1, 2, 6, 11, 17
Question 22
 For a normal population with µ = 40 and σ = 10 which of the following samples has the highest probability of being obtained?

a. 
M = 42 for a sample of n = 100 

b. 
M = 42 for a sample of n = 4 
[removed] 
c. 
M = 44 for a sample of n = 4 
[removed] 
d. 
M = 44 for a sample of n = 100 
Question 23
 The sum of the squared deviation scores is SS = 20 for a population of N = 5 scores. What is the variance for this population?
[removed] 
a. 
80 

b. 
100 

c. 
5 

d. 
4 
Question 24
 A linear regression equation has b = 3 and a = – 6. What is the predicted value of Y for X = 4?

a. 
= –21 

b. 
= 6 

c. 
This cannot be determined without additional information. 

d. 
= –2 
Question 25
 With α = .01 the twotailed critical region for a t test using a sample of n = 16 subjects would have boundaries of ____.

a. 
t = ±2.602 

b. 
t = ±2.947 

c. 
t = ±2.921 

d. 
t = ±2.583 
Question 26
 In a sample of n = 6 scores, the smallest score is X = 3, the largest score is X = 10, and the mean is M = 6. If the largest score is changed from X = 10 to X = 22, then what is the value of the new mean?

a. 
The mean is still M = 6. 

b. 
The mean is M = 8. 

c. 
The mean is M=10. 

d. 
The mean is M = 7. 
Question 27
 For the distribution in the following table, what is the 90^{th} percentile?
X c%
3034 100%
2529 90%
2024 60%
1519 20%

a. 
X = 29 

b. 
X = 29.5 

c. 
X = 25 

d. 
X = 24.5 
Question 28
 If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that m = 80?

a. 
M = 90 and small sample variance 

b. 
M = 85 and small sample variance 

c. 
M = 90 and large sample variance 

d. 
M = 85 and large sample variance 
Question 29
 For the following data, what is SS_{between subjects}?
Treatments
Subject I II III Ptotals
A 3 4 5 12 G = 27
B 1 1 4 6 ΣX^{2} = 109
C 2 1 6 9
T = 6 T = 6 T = 15
SS = 2 SS = 6 SS = 2
Question 30
 A set of 10 scores has SS = 90. If the scores are a sample, the sample variance is ____ and if the scores are a population, the population variance is ____.
[removed] 
a. 
s^{2} = 10; σ^{2} = 9 
[removed] 
b. 
s^{2} = 9; σ^{2} = 10 
[removed] 
c. 
s^{2} = 9; σ^{2} = 9 
[removed] 
d. 
s^{2} = 10; σ^{2} = 10 
Question 31
 For a bellshaped distribution with µ = 30, what is the most probable value for the mode?

a. 
0 

b. 
30 

c. 
greater than 30 

d. 
less than 30 
Question 32
 Which of the following is true for most distributions?

a. 
Around 30% of the scores will be located within one standard deviation of the mean. 

b. 
Around 90% of the scores will be located within one standard deviation of the mean. 

c. 
Around 70% of the scores will be located within one standard deviation of the mean. 

d. 
Around 50% of the scores will be located within one standard deviation of the mean. 
Question 33
 A researcher uses an analysis of variance to test for mean differences among three treatments with a sample of n = 12 in each treatment. The Fratio for this analysis would have which df values?

a. 
df = 2, 33 

b. 
df = 2, 36 

c. 
df = 2, 35 

d. 
df = 2, 11 
Question 34
 In a population with σ = 8, a score of X = 44 corresponds to a zscore of z = –0.50. What is the population mean?

a. 
μ = 48 

b. 
μ = 36 

c. 
μ = 40 

d. 
μ = 52 
Question 35
 A vertical line is drawn through a normal distribution at z = 0.80. What proportion of the distribution is on the righthand side of the line?

a. 
0.2119 

b. 
0.7881 

c. 
0.5762 

d. 
0.2881 
Question 36
 What is the value of ΣX^{2} for the following scores? Scores: 1, 0, 2, 4
Question 37
 A researcher conducts a repeatedmeasures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. What is the correct decision for a hypothesis test using α = .05?

a. 
Reject the null hypothesis with either a onetailed or a twotailed test. 

b. 
Fail to reject the null hypothesis with a onetailed test but reject with two tails. 

c. 
Reject the null hypothesis with a onetailed test but fail to reject with two tails. 

d. 
Fail to reject the null hypothesis with either a onetailed or a twotailed test. 
Question 38
 A distribution of scores has a mean of µ = 50. One new score is added to the distribution and the new mean is found to be µ = 48. From this result, you can conclude that the new score was ____.

a. 
greater than 50 

b. 
equal to 48 

c. 
less than 50 

d. 
between 50 and 52 
Question 39
 A researcher uses an anonymous survey to investigate the study habits of American college students. The entire group of American college students is an example of a ____.

a. 
sample 

b. 
statistic 

c. 
parameter 

d. 
population 
Question 40
 A multiple regression equation with two predictor variables is calculated for a set of scores. If the constant values in the equation are b_{1} = 2, b_{2} = –3, and a = 7, then what Y value would be predicted for an individual with X_{1} = 2 and X_{2} = 4?

a. 
41 

b. 
–1 

c. 
1 

d. 
17 
Question 41
 An independentmeasures study comparing two treatment conditions produces a t statistic with df = 18.If the two samples are the same size, how many participants were in each of the samples?
Question 42
 Two separate samples are being used to estimate the difference between population means for two treatment conditions. Which of the following would produce the widest confidence interval?

a. 
n_{1} =n_{2} = 20 with a pooled variance of 100 

b. 
n_{1} =n_{2} = 20 with a pooled variance of 10 

c. 
n_{1} =n_{2} = 10 with a pooled variance of 10 

d. 
n_{1} =n_{2} = 10 with a pooled variance of 100 
Question 43
 For independentmeasures ANOVA, individual differences contribute to the variance in the numerator and in the denominator of the Fratio. What happens to the individual differences in the denominator of the Fratio for repeatedmeasures ANOVA?

a. 
They are amplified in the denominator of the ratio. 

b. 
They are measured and subtracted out in of the analysis process. 

c. 
They do not exist because the same individuals participate in all of the treatments. 

d. 
They contribute to the variance in the denominator. 
Question 44
 If a frequency distribution is shown in a bar graph, what scale was used to measure the scores?

a. 
nominal 

b. 
ratio 

c. 
interval or ratio 

d. 
nominal or ordinal 
Question 45
 Given a population with mean m = 60, which of the following values for the population standard deviation would cause X = 68 to have the most extreme position in the distribution?

a. 
σ = 2 

b. 
σ = 5 

c. 
σ = 12 

d. 
σ = 3 
Question 46
 On an exam with μ = 52, you have a score of X = 56. Which of the following values for the standard deviation would give you the highest position in the class distribution?

a. 
σ = 8 

b. 
σ = 4 

c. 
σ = 10 
[removed] 
d. 
σ = 2 
Question 47
 What is indicated by a large value for the chisquare statistic?

a. 
There is a good fit between the sample data (observed values) and the null hypothesis. 

b. 
The sample data (observed values) do not match the null hypothesis. 

c. 
There is a good fit between the sample data (observed values) and the null hypothesis. 

d. 
The observed values from the sample data are consistently smaller than the expected values. 
Question 48
 The results from a research study indicate that adolescents who watch more violent content on television also tend to engage in more violent behavior than their peers. The correlation between amount of TV violent content and amount of violent behavior is an example of a ____.

a. 
correlation near one 

b. 
negative correlation 

c. 
correlation near zero 

d. 
positive correlation 
Question 49
 For an experiment involving three levels of factor A and three levels of factor B, with a sample of n = 8 in each treatment condition, what are the df values for the Fratio for the AxB interaction?

a. 
6, 63 

b. 
2, 63 

c. 
4, 63 

d. 
8, 63 
Question 50
 For repeatedmeasures ANOVA, the variability within treatments is divided into two components. What are they?

a. 
total variability and error 

b. 
between subjects and between treatments 

c. 
between treatments and error 

d. 
between subjects and error 
Question 51
 An analysis of variance comparing three treatment conditions produces df_{within} = 21. If the samples are all the same size, how many individuals are in each sample?
Question 52
 For the following distribution, what is the width of each class interval?
X f
2024 2
1519 5
1014 4
59 1
Question 53
 In a line graph showing the results from a twofactor experiment, the levels of factor B are presented on the Xaxis and separate lines are used to display the means for A1 and A2. If the points on the line for A1 are consistently five points higher than the corresponding point on the line for A2, what pattern of results is indicated?

a. 
an indication of an Aeffect but no indication of an interaction 

b. 
no indication of an interaction 

c. 
an indication of an Aeffect 

d. 
an indication of an interaction but no indication of an Aeffect 
Question 54
 For a sample of n = 30 scores, X = 45 corresponds to z = 1.50 and X = 40 corresponds to z = +1.00. What are the values for the sample mean and standard deviation?

a. 
M = 30 and s = 15 

b. 
M = 35 and s = 15 

c. 
M = 30 and s = 10 

d. 
M = 35 and s = 10 
Question 55
 A researcher obtains a Pearson correlation of r = 0.43 for a sample of n = 20 participants. For a twotailed test, which of the following accurately describes the significance of the correlation?

a. 
The correlation is equal to zero. 

b. 
The correlation is significant with either α = .05 or α = .01. 

c. 
The correlation is not significant with either α = .05 or α = .01. 

d. 
The correlation is significant with α = .05 but not with α = .01. 
Question 56
 For a population with µ = 80 and σ = 10, what is the X value corresponding to z = –0.50?

a. 
5 

b. 
85 

c. 
79.5 

d. 
75 
uestion 57
 A population with a mean of µ = 6 has ΣX = 42. How many scores are in the population?

a. 
N = 42/6 = 7 

b. 
N = 6*42 = 252 

c. 
N = 6/42 = 1/7 

d. 
N=42 
Question 58
 The results from a repeatedmeasures ANOVA are reported as, F(3, 24) = 3.75, p < .05. For this study, how many treatment conditions were compared?
uestion 59
 Which of the following is the standard error of estimate for a linear regression equation?

a. 
the square root of (SS_{residual}/(n – 2)) 

b. 
the square root of (SS_{regression}/(n – 3)) 

c. 
the square root of (SS_{residual}/(n – 3)) 

d. 
the square root of (SS_{regression}/(n – 2)) 
Question 60
 A researcher measures eye color for a sample of n = 50 people. Which measure of central tendency would be appropriate to summarize the measurements?

a. 
mean 

b. 
median 

c. 
mode 

d. 
weighted mean 
Question 61
 For a repeatedmeasures study comparing three treatment conditions with a sample of n = 4 participants, the participant totals (the P values) are 3, 6, 9, and 6. What is the value for SS_{between subjects}?
Question 62
 Which combination of factors is most likely to produce a significant value for an independentmeasures t statistic?

a. 
large samples and large variance 

b. 
small samples and large variance 

c. 
small samples and small variance 

d. 
large samples and small variance 
Question 63
 For an independentmeasures t statistic, what is the effect of increasing the number of scores in the samples?

a. 
Increase the likelihood of rejecting H_{0} and have little or no effect on measures of effect size. 

b. 
Increase the likelihood of rejecting H_{0} and increase measures of effect size. 

c. 
Decrease the likelihood of rejecting H_{0} and have little or no effect on measures of effect size. 

d. 
Increase the likelihood of rejecting H_{0} and decrease measures of effect size. 
Question 64
 Using zscores, a population with µ = 37 and s = 6 is standardized so that the new mean is µ = 50 and s = 10. After the standardization, one individual has a score of X = 55. What was this individual’s score in the original distribution?

a. 
X = 43 

b. 
X = 40 

c. 
It cannot be determined with the information given. 

d. 
X = 42 
Question 65
 A researcher is curious about the average monthly cell phone bill for all high school students in the state of Florida. If this average could be obtained, it would be an example of a ____.

a. 
statistic 

b. 
population 

c. 
parameter 

d. 
sample 
Question 66
 What happens to the expected value of M as sample size increases?

a. 
It also increases. 

b. 
The expected value does not change in a predictable manner when sample size increases. 

c. 
It decreases. 

d. 
It stays constant. 
Question 67
 A set of n = 15 pairs of scores (X and Y values) produces a correlation of r = 0.40. If each of the X values is multiplied by 2 and the correlation is computed for the new scores, what value will be obtained for the new correlation?

a. 
This cannot be determined without knowing all the X and Y scores. 

b. 
r = 0.40 

c. 
r = 0.80 

d. 
r = 0.20 
Question 68
 Two variables are said to interact when ____.

a. 
both variables produce a change in the subjects’ scores 

b. 
the two variables are differentially affected by a third variable 

c. 
the effect of one independent variable depends on the levels of the second variable 

d. 
both variables are equally influenced by a third factor 
Question 69
 A random sample of n = 4 scores is obtained from a population with a mean of µ = 80 and a standard deviation of σ = 10. If the sample mean is M = 90, what is the zscore for the sample mean?

a. 
z = 2.00 

b. 
z = 5.00 

c. 
z = 20.00 
z = 1.00 
· What term is used to identify the mean of the distribution of sample means?

a. 
the expected value of M 

b. 
the central limit mean 

c. 
the standard error of M 

d. 
the sample mean 
Question 71
 A repeatedmeasures analysis of variance produces SS_{within treatments} = 84 and SS_{between subjects} = 20. For this analysis, what is the value of SS_{error}?

a. 
64 

b. 
16 
[removed] 
c. 
24 
[removed] 
d. 
104 
Question 72
 The distance between the Y value in the data and the Y value predicted from the regression equation is known as the residual. What is the value for the sum of the squared residuals?

a. 
SS_{residual} = r^{2}(SS_{X}) 

b. 
SS_{residual} = (1 – r^{2})(SS_{X}) 

c. 
SS_{residual} = r^{2}(SS_{Y}) 

d. 
SS_{residual} = (1 – r^{2})(SS_{Y}) 
Question 73
 If the following seven scores are ranked from smallest to largest, then what rank should be assigned to a score of X = 1?
Scores: 1, 1, 1, 1, 3, 6, 6, 6, 9
Question 74
 What term is used to describe the shape of a distribution in which the scores pile up on the lefthand side of the graph and taper off to the right?

a. 
positively skewed 

b. 
negatively skewed 

c. 
normal 

d. 
symmetrical 
Question 75
 A research report describing the results from a repeatedmeasures study states: The data show no significant difference between the two treatments, t(10) = 1.65, p > .05. Based on this report, you can conclude that a total of ____ individuals participated in the research study.
Question 76
 A sample of n = 4 scores has SS = 48. What is the estimated standard error for the sample mean?
Question 77
 What is stated by the alternative hypothesis (H_{1}) for an ANOVA?

a. 
The beta estimate is significant. 

b. 
There are no differences between any of the population means. 

c. 
All of the population means are different from each other. 

d. 
At least one of the population means is different from another mean. 
Question 78
 Which of the following accurately describes the expected frequencies for a chisquare test?

a. 
They are always whole numbers. 

b. 
They are positive whole numbers. 

c. 
They can contain both positive and negative values. 

d. 
They can contain fractions or decimal values. 
Question 79
 The smallest score in a population is X = 5 and the largest score is X = 10. Based on this information, you can conclude that the____.

a. 
mean is greater than 10 

b. 
standard deviation is greater than 6 

c. 
standard deviation is less than 6 

d. 
standard deviation is smaller than 5 
Question 80
 What is the variance for the following population of scores? Scores: 5, 2, 5, 4

a. 
1.5 

b. 
6 

c. 
1.22 

d. 
2 
Question 81
 A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population. If the researcher uses a onetailed test with a = .01, then which of the following correctly identifies the critical region?

a. 
z < 2.33 

b. 
z < 2.58 

c. 
z > 2.33 

d. 
z > 2.58 
Question 82
 A researcher measures driving distance from college and weekly expense on gas for a group of commuting college students. What kind of correlation is likely to be obtained for these two variables?

a. 
a correlation near zero 

b. 
a negative correlation 

c. 
a positive correlation 

d. 
a correlation near one 
Question 83
 What is the mean for the following scores? Scores: 1, 6, 14
Question 84
 For a twofactor study with two levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, the two means for level A1 are 4 and 1, and the two means for level A2 are 3 and 2. For these data, what is the SS value for factor A (SS_{A})?

a. 
0 

b. 
250 

c. 
125 

d. 
50 
Question 85
 Which of the following accurately describes the chisquare test for goodness of fit?

a. 
It is similar to a correlation because it uses one sample to evaluate the relationship between two variables. 

b. 
It is similar to both a correlation and an independentmeasures t test because it can be used to evaluate a relationship between variables or a difference between populations. 

c. 
It is similar to an independentmeasures t test because it uses separate samples to evaluate the difference between separate populations. 

d. 
It is similar to a singlesample t test because it uses one sample to test a hypothesis about one population. 
researcher uses an anonymous survey to investigate the study habits of American college students. Based on the set of 56 surveys that were completed and returned, the researcher finds that these students spend an average of 4.1 hours each week working on course material outside of class. For this study, the set of 56 students who returned surveys is an example of a ____.

a. 
parameter 

b. 
population 

c. 
sample 

d. 
statistic 
Question 87
 One use of a regression equation is to increase the accuracy of predicting Y scores. What determines the proportion of the variability in the Y scores that is predicted by the regression equation?

a. 
r^{2} 

b. 
r 

c. 
1 – r 

d. 
1 – r^{2} 
Question 88
 For the repeatedmeasures t statistic, where n1 and n2 are the number of scores before and after treatment, and n = n_{1}= n_{2}, df = ____.

a. 
n_{1} + n_{2} – 1 

b. 
n_{1} + n_{2} – 2 

c. 
n – 2 

d. 
n – 1 
Question 89
 If an entire population with μ = 60 and s = 8 is transformed into zscores, then the distribution of zscores will have a mean of ____ and a standard deviation of ____.
a. 
60 and 1 

b. 
0 and 1 


c. 
0 and 8 

d. 
60 and 8 (unchanged) 
Question 90
 A population of scores has µ = 80. In this population, a score of X = 86 corresponds to z = +2.00. What is the population standard deviation?
Question 91
 For a twofactor study with two levels of factor A, two levels of factor B, and a separate sample of n = 10 participants in each treatment condition, the two means for level A1 are 4 and 1, and the two means for level A2 are 3 and 2. For these data, what is the value of SS_{between treatments}?

a. 
300 
b. 
40 

c. 
50 


d. 
10 
Question 92
 Under what circumstances is the pointbiserial correlation used?

a. 
when both X and Y are dichotomous variables 

b. 
in the same circumstances when a repeatedmeasures t test would be used 

c. 
when X consists of regular, numerical scores but Y is dichotomous 

d. 
when both X and Y are measured on an ordinal scale (ranks) 
Question 93
 The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 10 participants in each treatment. Note that several values are missing in the table. What is the missing value for SS_{total}?
Source SS df MS
Between 20 xx xx F = xx
Within xx xx 2
Total xx xx
Question 94
 A normal distribution has a mean of µ = 40 with σ = 10. What proportion of the scores in this distribution are smaller than X = 35?

a. 
0.9332 

b. 
0.3085 

c. 
0.6915 

d. 
0.0668 
Question 95
 A researcher reports an Fratio with df = 2, 40 from a repeatedmeasures ANOVA. How many treatment conditions were compared in this experiment?

a. 
4 

b. 
3 

c. 
41 
[removed] 
d. 
2 