# Psychology Statistics Midterm Study Guide

1. In the group of scores 2, 81, 82, 82, and 84, the outlier is __________.
1. 2
2. The distribution of the scores in most psychological research studies is _________.
1. unimodal
3. Use the following scenario to answer the question below: A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows. Ethnic Group A: N = 15 M = 55 S2 = 6.5 Ethnic Group B: N = 23 M = 51 S2 = 4.5 If the standard deviation of the distribution of the difference between means is 0.76, what is the t score?
1. (55 – 51) / 0.76 = 5.26
4. Use the following scenario to answer the question below: A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows. Ethnic Group A: N = 15 M = 55 S2 = 6.5 Ethnic Group B: N = 23 M = 51 S2 = 4.5 What is the pooled estimate of the population variance?
1. Correct [(14 / 36) (6.5)] + [(22 / 36) (4.5)] = 5.28
5. The ΣX for the scores 1, 1, 8, and 10 is
1. 20
6. The mode of the following scores 3, 4, 6, 7, 10, 10, and 30 is _________.
1. 10
7. Based on the scores 1, 9, 3, 6, 1, 2, 6, 2, 2, and 8, a score of 2 is the ________.
1. Mode
8. If the standard deviation is 4, the variance is
1. 16
9. Each of several patients is rated for their degree of depression, and if a particular patient's depression is rated 8 on a 20-point scale, 8 represents that patient's ___________.
1. Score
10. Which statement is true for the scores of 1, 2, 3, 4, 5, 5, 7, 8, 9, and 10?
1. The mean is greater than the median.
11. Consider the scores 2, 6, 7, 1, 7, 8, 5, and 4. Which of the following would be the correct second line of a frequency table?
1. 2 1 12.5%
12. If a difference between scores of 3 and 4 is the same as a difference between scores of 15 and 16, the variable being measured is __________.
1. equal interval
13. A psychologist studying the rate at which infants in three different countries vocalized distress obtained the scores below from each country. Which group of infants showed the highest mean rate of distress vocalization?

Country A 9, 9, 10, 13, 8, 8, 11, 11, 10, 7

Country B 15, 15, 16, 9, 14, 14, 17, 17, 16, 13

Country C 4, 6, 20, 17, 15, 21, 18, 18, 25, 2

1. Countries B and C were equally high
1. The mean of the scores 2, 2, 2, and 6 is __________.
1. 3
2. If the exact degree of difference between two scores has no meaning beyond the fact that one is higher than the other, the level of measurement is:
1. rank-order.
3. If an experimenter conducts a t-test for independent means and rejects the null hypothesis, the correct interpretation is that:
1. the mean of one sample is so far from the mean of the other sample that the samples must come from populations with different means.
4. Consider the scores 2, 9, 7, 6, 1, 9, 1, and 2. Which of the following would be the correct bottom line of a frequency table?
1. 9 2 25%
5. Which statement is only true for the t-test for dependent means rather than t-tests in general?
1. Pretest-posttest experimental designs are common.
6. Use the following scenario to answer the question below: A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows. Ethnic Group A: N = 15 M = 55 S2 = 6.5 Ethnic Group B: N = 23 M = 51 S2 = 4.5
1. (15 – 1) + (23 – 1) = 36
7. A normal curve is
1. bimodal

Parameters

Population mean = μ = ( Σ Xi ) / N

Population standard deviation = σ = sqrt [ Σ ( Xi - μ )2 / N ]

Population variance = σ2 = Σ ( Xi - μ )2 / N

Variance of population proportion = σP2 = PQ / n

Standardized score = Z = (X - μ) / σ

Population correlation coefficient = ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] }

Statistics

Sample mean = x = ( Σ xi ) / n

Sample standard deviation = s = sqrt [ Σ ( xi - x )2 / ( n - 1 ) ]

Sample variance = s2 = Σ ( xi - x )2 / ( n - 1 )

Variance of sample proportion = sp2 = pq / (n - 1)

Pooled sample proportion = p = (p1 * n1 + p2 * n2) / (n1 + n2)

Pooled sample standard deviation = sp = sqrt [ (n1 - 1) * s12 + (n2 - 1) * s22 ] / (n1 + n2 - 2) ]

Sample correlation coefficient = r = [ 1 / (n - 1) ] * Σ { [ (xi - x) / sx ] * [ (yi - y) / sy ] }

Correlation

Pearson product-moment correlation = r = Σ (xy) / sqrt [ ( Σ x2 ) * ( Σ y2 ) ]

Linear correlation (sample data) = r = [ 1 / (n - 1) ] * Σ { [ (xi - x) / sx ] * [ (yi - y) / sy ] }

Linear correlation (population data) = ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] }

Linear Regression

Simple linear regression line: ŷ = b0 + b1x

Regression coefficient = b1 = Σ [ (xi - x) (yi - y) ] / Σ [ (xi - x)2]

Regression slope intercept = b0 = y - b1 * x

Regression coefficient = b1 = r * (sy / sx)

Standard error of regression slope = sb1 = sqrt [ Σ(yi - ŷi)2 / (n - 2) ] / sqrt [ Σ(xi - x)2 ]

Counting Probability

n factorial: n! = n * (n-1) * (n - 2) * . . . * 3 * 2 * 1. By convention, 0! = 1.

Permutations of n things, taken r at a time: nPr = n! / (n - r)!

Combinations of n things, taken r at a time: nCr = n! / r!(n - r)! = nPr / r!

Rule of addition: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Rule of multiplication: P(A ∩ B) = P(A) P(B|A)

Rule of subtraction: P(A') = 1 - P(A)

Random Variables

Expected value of X = E(X) = μx = Σ [ xi * P(xi) ]

Variance of X = Var(X) = σ2 = Σ [ xi - E(x) ]2 * P(xi) = Σ [ xi - μx ]2 * P(xi)

Normal random variable = z-score = z = (X - μ)/σ

Chi-square statistic = Χ2 = [ ( n - 1 ) * s2 ] / σ2

f statistic = f = [ s12/σ12 ] / [ s22/σ22 ]

Expected value of sum of random variables = E(X + Y) = E(X) + E(Y)

Expected value of difference between random variables = E(X - Y) = E(X) - E(Y)

Variance of the sum of independent random variables = Var(X + Y) = Var(X) + Va

Sample Distribution

Mean of sampling distribution of the mean = μx = μ

Mean of sampling distribution of the proportion = μp = P

Standard deviation of proportion = σp = sqrt[ P * (1 - P)/n ] = sqrt( PQ / n )

Standard deviation of the mean = σx = σ/sqrt(n)

Standard deviation of difference of sample means = σd = sqrt[ (σ12 / n1) + (σ22 / n2) ]

Standard deviation of difference of sample proportions = σd = sqrt{ [P1(1 - P1) / n1] + [P2(1 - P2) / n2] }

## The correct answer is in bold

Q:In an analysis of variance, if the null hypothesis is true, then:

the within-groups estimate of the population variance is smaller than the between-groups estimate.

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the research hypothesis can also be true.

fewer participants can be included in the experiment.

there is less variance among means of samples than if the null hypothesis were not true.

the within-groups estimate of the population variance is smaller than the between-groups estimate.

Q: In a distribution of Z-scores, the mean is always:

10

1

0

50

Q: In a 2 × 3 × 3 analysis of variance, the number of cells is __________.

18

Q: In an analysis of variance with a within-groups variance estimate of 8.5 and a between-groups variance estimate of 5.3, the F ratio is:

5.3 / 8.5 = 0.62

8.5 / 5.3 = 1.60

√5.3 / 8.5 = 0.27

√8.5 / 5.3 = 0.55

Q The scenarios below are possible results of a study in which participants completed a measure of how important religion was to them personally. Participants are either from a rural or urban area and are either poor or rich. Which of the following interpretations is consistent with Scenario A?

Religion is more important to poor people when they live in rural areas. In the urban areas, poor people are socialized to be more like rich people, who are less religious, regardless of where they live.

Rich people, regardless of where they live, value religion moderately. Poor people value religion more in urban centers than in rural areas because it is more accessible.

People who live in the urban areas need religion more than people in rural areas, regardless of how rich or poor they are.

Poor people in urban areas have a harder time than people in rural areas, so they value religion more. Rich people who move to rural areas are trying to get away from their materialistic lifestyle and tend to be more religious.

Q: A study exploring the relationship between financial security (shaky, stable, or very secure) and annual income (low, moderate, or high) on satisfaction with life is an example of a two-way factorial design, specifically a ___ × ___ factorial design. (Give numbers.)

3x3

Q: Your sample of 12 people is being compared to a known population with a mean of 200 and a variance of 36, which makes the variance of the distribution of means ______.

3.0

Q: A population is normally distributed with μ = 50, σ = 8, and N = 10. The shape of the distribution of means in this example is __________.

Bell Shaped

Q: The scenarios below are possible results of a study in which participants completed a measure of how important religion was to them personally. Participants are either from a rural or urban area and are either poor or rich. Which of the following statements is true based on the information presented in Scenario C?

On average, religion is more important to rich people than to poor people.

The column means show that religion is more important to poor people.

The row means show that there is no difference between rich and poor in their average interest in religion.

There is a clear interaction effect in which poor people value religion more in urban areas, while rich people value it more in rural areas.

Q: A population is normally distributed with μ = 50, σ = 8, and N = 10. The variance of the distribution of means = __________.

6.4

Q: The variance of a distribution of Z-scores is always:

(Z) (M + SD)

0

1

Q: The raw score that corresponds to a Z-score of 2.0 obtained from a distribution with a mean of 80 and a standard deviation of 10 is _____.

100

Q: A population is normally distributed with μ = 50, σ = 8, and N = 10. The mean of the distribution of means = __________.

50

Q: The conventional levels of significance in hypothesis testing in psychology are:

.001 and .01

.01 and .05

.10, .20, and .30

.05, .25, and .95

Q: The scenarios below are possible results of a study in which participants completed a measure of how important religion was to them personally. Participants are either from a rural or urban area and are either poor or rich. Which statement is true about Scenario B?

There is a moderate interaction effect.

Religion is consistently more important for rich people than for poor people, regardless of where they live.

Religion is more important to people who live in the urban areas, regardless of their wealth

Religion is particularly important to people who are both poor and live in rural areas.

Q: The statistical procedure ensures that the alpha level for any given planned contrast will not exceed .05 is ______.

Bonferroni

Q: In an analysis of variance, you reject the null hypothesis when the F ratio is:

negative

much larger than 1

equal to the t score

smaller than 1

Q: If the mean score on a stress scale is 5, the standard deviation is 2, and the distribution is normal, what would be the mean value when converted to a Z-distribution?

0

2

5

Not enough information to make a determination

Q: When a psychologist sets up a hypothesis testing problem, the intent is to:

test for two effects, the predicted behavior and the opposite behavior.

determine whether the predicted behavior will occur.

determine whether the opposite of the predicted behavior will occur.

test for two effects, the predicted behavior and the opposite behavior.

test the difference between two populations, regardless of the predicted behavior.

Q: In an analysis of variance with a between-groups population variance estimate of 30 and a within-groups estimate of 25, the F ratio is:

25 / (30–25) = 5.00

(30–25) / 30 = 0.17

25 / 30 = 0.83

30 / 25 = 1.20