Question

#1 Assume that a new interpretation of the frustration aggression hypothesis says that it is not all people who become aggressive when frustrated, but only those who have been brought up in a home where physical punishment is used become aggressive when frustrated. To test this hypothesis, two groups of children are found. One group is brought up in homes where physical punishment is used as a form of discipline. The other group consists of children whose parents chastise them verbally, or remove privileges, but do not actually hit them. The children are all placed in a situation where they are frustrated in the course of play activity. The play situation includes a doll that the children have in their hands at the time of the frustration experience. The experimenter intends to have judges classify the children as either physically aggressive or not, physically aggressive toward the doll (at the time of frustration). Which statistic would be used?

		Z-test
		One Sample t-test
		Independent groups t-test
		Dependent groups t-test
		One Factor ANOVA
		Two factor ANOVA
		t-test for r > 0
		Chi-square test
		Phi Coefficient
		Cramer’s Phi
		Point Biserial r
		Eta-squared
		r-squared or r

#2 A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-square test for independence is used to examine the distribution of individuals in a 2×3 matrix of categories. Which test has the larger value for df?

	a.	​The test for independence
	b.	​Both tests have the same df.
	c.	​The test for goodness of fit
	d.	​The df value depends on the sizes of the samples that are used.

#3 A chi-square test for independence is being used to evaluate the relationship between two variables. If the test has df = 2, what can you conclude about the two variables?

	a.	​One variable consists of 2 categories and the other consists of 4 categories.
	b.	​Both variables consist of 2 categories.
	c.	​Both variables consist of 3 categories.
	d.	​One variable consists of 2 categories and the other consists of 3 categories.

#4 Under what circumstances will the chi-square test for goodness of fit produce a large value for the chi-square?

	a.	​When there is a large difference between the sample mean and the population mean
	b.	​When the sample mean is close to the population mean
	c.	​When the sample proportions are much different than the hypothesized population proportions
	d.	When the sample proportions match the hypothesized population proportions​

#5 For the chi-square test for goodness of fit, the researcher must select a sample with an equal number of individuals in each category.

True

False

#6 A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-square test for independence is used to examine the distribution of individuals in a 2×2 matrix of categories. Which test has the larger value for df?

	a.	​The test for goodness of fit
	b.	​The test for independence
	c.	​The df value depends on the sizes of the samples that are used.
	d.	​Both tests have the same df.

#7 What is referred to by the term expected frequencies?

	a.	​The frequencies that are hypothesized for the population being examined
	b.	​The frequencies found in the population being examined
	c.	​The frequencies computed from the null hypothesis
	d.	​The frequencies found in the sample data

#8 The observed frequencies for a chi-square test can be fractions or decimal values.

True

False

#9 The expected frequencies for a chi-square test are always whole numbers (no fractions or decimals).

True

False

#10 For a chi-square test, the observed frequencies are obtained from the sample.

True

False

#11 A researcher used a sample of n = 60 individuals to determine whether there are any preferences among four brands of pizza. Each individual tastes all four brands and selects his/her favorite. If the data are evaluated with a chi-square test for goodness of fit using α = .05, then how large does the chi-square statistic need to be to reject the null hypothesis?

	a.	​Greater than 79.08
	b.	​Greater than 7.81
	c.	​Less than 7.81
	d.	​Less than 79.08

#12 In general, a large value for chi-square indicates a good fit between the sample data and the null hypothesis.

True

False

#13 A chi-square test for independence is used to evaluate the relationship between two variables. If both variables are classified into 2 categories, then what is the df value for the chi-square statistic?

	a.	​3
	b.	​2
	c.	​Cannot determine the value of df from the information provided
	d.	​1

#14 For the expected frequencies in a chi-square test for independence, the proportions for any row are the same as the proportions in every other row.

True

False

#15 ​ Which of the following best describes the possible values for a chi-square statistic?

	a.	​Chi-square can be either positive or negative but is always a whole number.
	b.	​Chi-square is always a positive whole number.
	c.	​Chi-square is always positive but can contain fractions or decimal values.
	d.	​Chi-square can be either positive or negative and can contain fractions or decimals.

Answer 1

Solution

Q1

Third Option Answer 1

Explanation

There are just 2 groups whose means are tested for equality and the two groups are not related to each other.

Q2

Option b Answer 2

Explanation

For the first, 3 categoties are compared and so df = 2. For the second, the matrix is 2 x 3 and so df = (1 - 1) x (3 - 1) = 2

Q3

Option d Answer 3

Explanation

Independence chi-square on a tangency table with r rows and c columns, the df = (r - a) x (c - 1). If this is 2, the only possibility is r = 2 and c = 3 or vice-versa.

Q4

Option c Answer 4

Explanation

χ² = ∑{(O - E)²/E}. So, as (O - E) gets larger, χ² gets larger.

Q5

Option False Answer 5

Explanation

It is not necessary to have equal sample sizes.

Q6

Option a Answer 6

Explanation

See Answer 2

Q7

Option c Answer 7

Explanation

E is computed based on null hypothesis and the sample size.

Q8

Option False Answer 8

Explanation

Frequency cannot be non-integer when it is observed since the number of times something has occurred.

However, expected frequency can be a non-integer since is calculated.

Q9

Option False Answer 9

Explanation

See Answer 8

Q10

Option True Answer 10

Explanation

Very name ‘observed’ => from sample.

Q11

Option b Answer 11

Explanation

df is 3 (number of comparisons - 1). Upper 5% point of χ²₃= 7.81. [79.08 is the upper 5% point of χ²₆₀]

Q12

Option False Answer 12

Explanation

See Answer 4

Q13

Option d Answer 13

Explanation

See Answer 2 or 3

Q14

Option False Answer 14

Explanation

E = (row total x column total)/grand total and so depends on the row.

Q15

Option c Answer 15

Explanation

χ²is a square and hence cannot be negative. It is calculated from ∑{(O - E)²/E} which can take integer and non-integer values.

DONE