# Psyk500 study guide | Mathematics homework help

Question 1

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

1. In analysis of variance, each independent variable is referred to as a ____.
 a. stage [removed] b. comparison c. factor [removed] d. level

Question 3

1. Which outcome is expected if the null hypothesis is true for an analysis of variance?
 a. SSbetween should be about the same size as SSwithin. b. MSbetween should be about the same size as MSwithin. [removed] c. SSbetween should be about the same size as SStotal. [removed] d. MSbetween should be about the same size as MStotal.

Question 4

1. 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

1. A sample of difference scores has a mean of MD = 5 with a variance of s2 = 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

1. 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

1. The following X and Y scores produce SSX = 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

1. For a repeated-measures study comparing three treatment conditions with a sample of n = 4 participants, what are the degrees of freedom for the repeated-measures F-ratio?
 [removed] a. 2, 11 b. 2, 6 c. 2, 9 [removed] d. 3, 11

Question 9

1. 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

1. The percentage of variance accounted for by the treatment effect is usually known as _____ in published reports of ANOVA results.
 a. η2 b. α2 c. σ2 d. µ2

Question 12

1. 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

1. In a two-factor 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

1. A repeated-measures ANOVA has SSwithin treatments = 26 and SSbetween subjects = 12. For this analysis, what is the value for SSerror?

Question 15

1. For a population with a standard deviation of σ = 6, what is the z-score 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

1. A sample consists of n = 16 scores. How many of the scores are used to calculate the range?

Question 17

1. A multiple-choice 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. 0.5 d. 0.5675

Question 18

1. A hypothesis test produces a t statistic of t = 2.20. If the researcher is using a two-tailed 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

1. 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 Y-score variance, MSregression?
 a. 19 b. 18 c. 1 [removed] d. 2

Question 20

1. 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

1. What is the median for the following set of scores? Scores: 1, 2, 6, 11, 17

Question 22

1. 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

1. 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

1. 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

1. With α = .01 the two-tailed 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

1. 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

1. For the distribution in the following table, what is the 90th percentile?

X            c%

30-34   100%

25-29    90%

20-24   60%

15-19   20%

 a. X = 29 b. X = 29.5 c. X = 25 d. X = 24.5

Question 28

1. 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

1. For the following data, what is SSbetween subjects?

Treatments

Subject        I           II           III     P-totals

A                3            4            5             12         G = 27

B                1            1            4               6        ΣX2 = 109

C                2            1            6               9

T = 6       T = 6           T = 15

SS = 2     SS = 6         SS = 2

Question 30

1. 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. s2 = 10; σ2 = 9 [removed] b. s2 = 9; σ2 = 10 [removed] c. s2 = 9; σ2 = 9 [removed] d. s2 = 10; σ2 = 10

Question 31

1. For a bell-shaped 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

1. 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

1. 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 F-ratio 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

1. In a population with σ = 8, a score of X = 44 corresponds to a z-score of z = –0.50. What is the population mean?
 a. μ = 48 b. μ = 36 c. μ = 40 d. μ = 52

Question 35

1. A vertical line is drawn through a normal distribution at z = 0.80. What proportion of the distribution is on the right-hand side of the line?
 a. 0.2119 b. 0.7881 c. 0.5762 d. 0.2881

Question 36

1. What is the value of ΣX2 for the following scores? Scores: 1, 0, 2, 4

Question 37

1. A researcher conducts a repeated-measures 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 one-tailed or a two-tailed test. b. Fail to reject the null hypothesis with a one-tailed test but reject with two tails. c. Reject the null hypothesis with a one-tailed test but fail to reject with two tails. d. Fail to reject the null hypothesis with either a one-tailed or a two-tailed test.

Question 38

1. 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

1. 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

1. A multiple regression equation with two predictor variables is calculated for a set of scores. If the constant values in the equation are b1 = 2, b2 = –3, and a = 7, then what Y value would be predicted for an individual with X1 = 2 and X2 = 4?
 a. 41 b. –1 c. 1 d. 17

Question 41

1. An independent-measures 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

1. 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. n1 =n2 = 20 with a pooled variance of 100 b. n1 =n2 = 20 with a pooled variance of 10 c. n1 =n2 = 10 with a pooled variance of 10 d. n1 =n2 = 10 with a pooled variance of 100

Question 43

1. For independent-measures ANOVA, individual differences contribute to the variance in the numerator and in the denominator of the F-ratio. What happens to the individual differences in the denominator of the F-ratio for repeated-measures 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

1. 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

1. 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

1. 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

1. What is indicated by a large value for the chi-square 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

1. 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

1. 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 F-ratio for the AxB interaction?
 a. 6, 63 b. 2, 63 c. 4, 63 d. 8, 63

Question 50

1. For repeated-measures 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

1. An analysis of variance comparing three treatment conditions produces dfwithin = 21. If the samples are all the same size, how many individuals are in each sample?

Question 52

1. For the following distribution, what is the width of each class interval?

X         f

20-24   2

15-19     5

10-14   4

5-9       1

Question 53

1. In a line graph showing the results from a two-factor experiment, the levels of factor B are presented on the X-axis 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 A-effect but no indication of an interaction b. no indication of an interaction c. an indication of an A-effect d. an indication of an interaction but no indication of an A-effect

Question 54

1. 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

1. A researcher obtains a Pearson correlation of r = 0.43 for a sample of n = 20 participants. For a two-tailed 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

1. 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

1. 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

1. The results from a repeated-measures ANOVA are reported as, F(3, 24) = 3.75, p < .05. For this study, how many treatment conditions were compared?

uestion 59

1. Which of the following is the standard error of estimate for a linear regression equation?
 a. the square root of (SSresidual/(n – 2)) b. the square root of (SSregression/(n – 3)) c. the square root of (SSresidual/(n – 3)) d. the square root of (SSregression/(n – 2))

Question 60

1. 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

1. For a repeated-measures 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 SSbetween subjects?

Question 62

1. Which combination of factors is most likely to produce a significant value for an independent-measures 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

1. For an independent-measures t statistic, what is the effect of increasing the number of scores in the samples?
 a. Increase the likelihood of rejecting H0 and have little or no effect on measures of effect size. b. Increase the likelihood of rejecting H0 and increase measures of effect size. c. Decrease the likelihood of rejecting H0 and have little or no effect on measures of effect size. d. Increase the likelihood of rejecting H0 and decrease measures of effect size.

Question 64

1. Using z-scores, 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

1. 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

1. 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

1. 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

1. 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

1. 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 z-score 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

1. A repeated-measures analysis of variance produces SSwithin treatments = 84 and SSbetween subjects = 20. For this analysis, what is the value of SSerror?
 a. 64 b. 16 [removed] c. 24 [removed] d. 104

Question 72

1. 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. SSresidual = r2(SSX) b. SSresidual = (1 – r2)(SSX) c. SSresidual = r2(SSY) d. SSresidual = (1 – r2)(SSY)

Question 73

1. 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

1. What term is used to describe the shape of a distribution in which the scores pile up on the left-hand side of the graph and taper off to the right?
 a. positively skewed b. negatively skewed c. normal d. symmetrical

Question 75

1. A research report describing the results from a repeated-measures 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

1. A sample of n = 4 scores has SS = 48. What is the estimated standard error for the sample mean?

Question 77

1. What is stated by the alternative hypothesis (H1) 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

1. Which of the following accurately describes the expected frequencies for a chi-square 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

1. 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

1. 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

1. 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 one-tailed 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

1. 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

1. What is the mean for the following scores? Scores: 1, 6, 14

Question 84

1. For a two-factor 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 (SSA)?
 a. 0 b. 250 c. 125 d. 50

Question 85

1. Which of the following accurately describes the chi-square 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 independent-measures t test because it can be used to evaluate a relationship between variables or a difference between populations. c. It is similar to an independent-measures t test because it uses separate samples to evaluate the difference between separate populations. d. It is similar to a single-sample 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

1. 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. r2 b. r c. 1 – r d. 1 – r2

Question 88

1. For the repeated-measures t statistic, where n1 and n2 are the number of scores before and after treatment, and n = n1= n2, df = ____.
 a. n1 + n2 – 1 b. n1 + n2 – 2 c. n – 2 d. n – 1

Question 89

1. If an entire population with μ = 60 and s = 8 is transformed into z-scores, then the distribution of z-scores 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

1. 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

1. For a two-factor 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 SSbetween treatments?
 a. 300 b. 40 c. 50 d. 10

Question 92

1. Under what circumstances is the point-biserial correlation used?
 a. when both X and Y are dichotomous variables b. in the same circumstances when a repeated-measures 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

1. 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 SStotal?

Source             SS        df         MS

Between           20        xx        xx        F = xx

Within              xx        xx        2

Total                xx        xx

Question 94

1. 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

1. A researcher reports an F-ratio with df = 2, 40 from a repeated-measures ANOVA. How many treatment conditions were compared in this experiment?
 a. 4 b. 3 c. 41 [removed] d. 2