Question 1

A study tests the difference between 20 Democrats and 20 Republicans. In this example, the degrees of freedom is equal to ______.
A) 18
B) 19
C) 38
D) 39

Accepted Answer

The degrees of freedom (df) in a two-sample t-test is calculated as follows:

df = n1 + n2 - 2

where n1 is the sample size of Group 1 (Democrats) and n2 is the sample size of Group 2 (Republicans).

In this case, n1 = 20 and n2 = 20, so:

df = 20 + 20 - 2 = 38

Therefore, the correct answer is C (38).

Question 2

A researcher calculates the t-test for independent means and reports the following result: t(48) = 2.97, p < .01. This research study consisted of a TOTAL of ______ participants.
A) 25
B) 48
C) 49
D) 50

Accepted Answer

The t-test results include the degrees of freedom (df), which is calculated by adding the sample sizes for both groups subtracted by 2. In this case, the df is 48, which means that the total number of participants in the study is 50 (48 + 2). Therefore, the correct answer is D.

Question 3

A researcher calculates the t-test for independent means and reports the following result: t(24) = 2.16, p < .05. This research study consisted of a TOTAL of ______ participants.
A) 26
B) 25
C) 24
D) 23

Accepted Answer

The degrees of freedom (df) for a t-test for independent means is calculated as n1 + n2 - 2, where n1 and n2 are the sample sizes of the two groups. Given that df = 24, solving for n1 + n2 gives us 26 participants in total.

Question 4

A researcher hypothesizes that children from middle class families have higher education levels than children from lower class families. In conducting an analysis to test this hypothesis, how might the alternative hypothesis be stated?
A) H1: μD = 0
B) H1: μ Middle Class > μ Lower Class
C) H1: μ Middle Class ≠ μ Lower Class
D) H1: μ Middle Class < μ Lower Class

Accepted Answer

The alternative hypothesis should state that there is a difference in education levels between middle class and lower class children, with the directionality being that the middle class has higher levels. Therefore, option B is the best choice as it clearly states this directionality. Option C is also possible, but it is not as specific regarding the directionality. Options A and D are incorrect as they do not take into account the comparison between the two groups.

Question 5

In testing the difference between two means, what is implied by the alternative hypothesis (H₁)? A) μ₁ = μ₂ B) μ₁ - μ₂ = 0 C) μ₁ - μ₂ ≠ 0 D)

Accepted Answer

The alternative hypothesis states that there is a difference between the means of the two groups being compared, which is represented by the inequality symbol ≠ (not equal to). Therefore, choice C is the best choice. Choices A and B do not reflect the alternative hypothesis, and choice D appears to be a random string of characters.

Question 6

A study compares the means of two groups, each having N = 11. If the standard deviations of the two groups are 5.00 and 3.00, what is the value for the standard error of the difference  ?
A) .60
B) .85
C) 1.76
D) 3.09

Accepted Answer

The formula for standard error of the difference between two means is: 
Standard Error = sqrt[(s1^2/N1) + (s2^2/N2)]
Plugging in the values, we get: 
Standard Error = sqrt[(5^2/11) + (3^2/11)] = 1.76. Therefore, the answer is C.

Question 7

A researcher states the following hypotheses: H₀: μDogs = μCats and H₁: μDogs ≠ μ Cats. Assuming she collects data from 9 dogs and 9 cats, what is the appropriate critical value? A) 1.734 B) 2.120 C) 2.110 D) 2.101

Accepted Answer

Since the alternative hypothesis includes the "not equal to" symbol, this indicates a two-tailed test. With a sample size of 9 for both dogs and cats, the appropriate critical value at a significance level of 0.05 is t = 2.120 (from a t-distribution with 16 degrees of freedom). Therefore, the correct answer is B.

Question 8

A study compares the means of two groups, each having N = 15. If the standard deviations of the two groups are 1.67 and 2.98, what is the value for the standard error of the difference  ?
A) .19
B) .778
C) .880
D) .882

Accepted Answer

The answer of A study compares the means of two...

Question 9

A researcher states the following hypotheses: H₀: μMales = μ Females and H₁: μMales ≠ μFemales. Assuming she collects data from 15 males and 15 females, what is the appropriate critical value? A) 1.697 B) 1.701 C) 2.042 D) 2.048

Accepted Answer

The appropriate critical value is based on a two-tailed t-test with a significance level (usually 0.05) and degrees of freedom calculated as (n1 + n2 - 2) = 28. For df = 28, the critical value is approximately 2.048.

Question 10

A study compares the means of two groups, each having N = 20. If the standard deviations of the two groups are 10.00 and 6.00, what is the value for the standard error of the difference  ?
A) .89
B) 2.61
C) 5.43
D) 6.80

Accepted Answer

The standard error of the difference between means is calculated as the square root of [(SD1^2/N1) + (SD2^2/N2)]. Substituting the given values, we get the standard error as square root of [(10^2/20) + (6^2/20)] = 2.61. Therefore, the correct answer is B.

Question 11

A researcher comparing the means of two groups calculates the t-test for independent means and reports the following result: t(32) = -3.54, p <.01. This research study consisted of a TOTAL of ______ participants.
A) 16
B) 30
C) 32
D) 34

Accepted Answer

The "(32)" in t(32) indicates the degrees of freedom, which is calculated by subtracting 1 from the total number of participants in both groups. The formula for degrees of freedom for independent t-test is (n1 + n2) - 2. So, (n1 + n2) - 2 = 32 which gives us (n1 + n2) = 34. Since we know the two groups have equal sample sizes, the total number of participants in the study would be 34 divided by 2, which is 17 participants per group.

Question 12

A researcher comparing the means of two groups calculates the t-test for independent means and reports the following result: t(22) = -3.54, p <.01. This research study consisted of a TOTAL of ______ participants.
A) 20
B) 22
C) 24
D) 26

Accepted Answer

The t-test for independent means indicates that there were two groups in the study. The degrees of freedom (df) is 22, which means that the total number of participants in the study was 22 + 22 = 44. Therefore, the answer is C) 24, which is the closest even number to half of the total number of participants (44/2=22) and represents the sample size of each group.

Question 13

A study compares the means of two groups, each having N = 10. If the standard deviations in the two groups are 4.00 and 6.00, what is the value for the standard error of the difference  ?
A) 2.28
B) 1.00
C) 10.00
D) 5.20

Accepted Answer

The answer of A study compares the means of two...

Question 14

A study tests the difference between 15 ants and 15 ladybugs. In this example, the degrees of freedom is ______.
A) 14
B) 15
C) 28
D) 30

Accepted Answer

The degrees of freedom for an independent samples t-test is calculated as follows: DF = N1 + N2 - 2, where N1 and N2 are the sample sizes of the two groups being compared. In this case, N1 = 15 and N2 = 15, so DF = 15 + 15 - 2 = 28. Therefore, the correct answer is C).

Question 15

In testing the difference between two means, which of the following is implied by the alternative hypothesis (H₁)? A) The two population means are equal to each other. B) The difference between the two population means is equal to 0. C) The difference between the two population means is not equal to 0. D) The difference between the two sample means is equal to 0.

Accepted Answer

The alternative hypothesis H₁ states that the difference between the two population means is not equal to 0. This implies that we are testing for a significant difference between the two sample means and rejecting the null hypothesis (that the two population means are equal). Option A is incorrect because it refers to the null hypothesis. Option B is incorrect because it states that the difference between the two population means is equal to 0, which is the null hypothesis. Option D is incorrect because it refers to the sample means, not the population means.

Question 16

A researcher comparing the means of two groups calculates the t-test for independent means and reports the following result: t(28) = 2.11, p <.05. This research study consisted of a TOTAL of ______ participants.
A) 14
B) 15
C) 28
D) 30

Accepted Answer

The degrees of freedom for the t-test are calculated as the sum of the sample sizes minus 2 (df = n1 + n2 - 2). In this case, we only have information about one sample size (n1), which is equal to 28 (based on the reported degrees of freedom). Therefore, the total sample size would be equal to n1 + n2 = 28 + n2. We cannot determine n2 with the information given. However, we do know that the total sample size must be greater than 28, so the closest option is D with 30 participants.

Question 17

A researcher states the following hypotheses: H₀: μ Freshmen = μ Sophomores and H₁: μ Freshmen ≠ μ Sophomores. Assuming she collects data from 13 freshmen and 13 sophomores, what is the appropriate critical value? A) 1.706 B) 1.711 C) 2.056 D) 2.064

Accepted Answer

The answer of A researcher states the following hypotheses: H₀:...

Question 18

A researcher states the following hypotheses: H₀: μCity1 = μCity2 and H₁: μCity1 > μCity2. Assuming she collects data from 30 people who live in city 1 and 30 people who live in city 2, what is the appropriate critical value? A) 1.672 B) 1.700 C) 1.960 D) 2.002

Accepted Answer

The appropriate critical value for a one-tailed test (since the hypothesis is μCity1 > μCity2) with a sample size of 30 from each city (total n = 60) and assuming an alpha level of 0.05 is 1.672. This is because with a total sample size of 60, the degrees of freedom (df) would be 58 (n1 + n2 - 2), and for a one-tailed test at the 0.05 significance level, the critical value from the t-distribution table approximates to 1.672.

Question 19

In testing the difference between two sample means  , the greater the difference between the two means, the more the value of the t-statistic (t) differs from ______.
A) 0
B) μ
C) the alternative hypothesis
D) the region of rejection

Accepted Answer

The t-statistic is calculated as the difference between the sample means divided by the standard error of the difference. As the difference between the sample means gets larger, the numerator of this fraction gets larger and therefore the value of the t-statistic gets further away from 0.

Question 20

A study compares the means of two groups, each having N = 10. If the standard deviations in the two groups are 3.00 and 5.00, what is the value for the standard error of the difference  ?
A) .89
B) 1.84
C) 3.40
D) 8.00

Accepted Answer

The formula for standard error of the difference is:
SE = sqrt((s1^2 / N1) + (s2^2 / N2))
SE = sqrt((3^2 / 10) + (5^2 / 10))
SE = sqrt(9/10 + 25/10)
SE = sqrt(34/10)
SE = 1.84

Quiz 9: Testing the Difference Between Two Means

A study tests the difference between 20 Democrats and 20 Republicans. In this example, the degrees of freedom is equal to ______.

A researcher calculates the t-test for independent means and reports the following result: t(48) = 2.97, p < .01. This research study consisted of a TOTAL of ______ participants.

A researcher calculates the t-test for independent means and reports the following result: t(24) = 2.16, p < .05. This research study consisted of a TOTAL of ______ participants.

A researcher hypothesizes that children from middle class families have higher education levels than children from lower class families. In conducting an analysis to test this hypothesis, how might the alternative hypothesis be stated?

In testing the difference between two means, what is implied by the alternative hypothesis (H₁) ?

A study compares the means of two groups, each having N = 11. If the standard deviations of the two groups are 5.00 and 3.00, what is the value for the standard error of the difference ?

A researcher states the following hypotheses: H₀: μDogs = μCats and H₁: μDogs ≠ μ Cats. Assuming she collects data from 9 dogs and 9 cats, what is the appropriate critical value?

A study compares the means of two groups, each having N = 15. If the standard deviations of the two groups are 1.67 and 2.98, what is the value for the standard error of the difference ?

A researcher states the following hypotheses: H₀: μMales = μ Females and H₁: μMales ≠ μFemales. Assuming she collects data from 15 males and 15 females, what is the appropriate critical value?

A study compares the means of two groups, each having N = 20. If the standard deviations of the two groups are 10.00 and 6.00, what is the value for the standard error of the difference ?

A researcher comparing the means of two groups calculates the t-test for independent means and reports the following result: t(32) = -3.54, p <.01. This research study consisted of a TOTAL of ______ participants.

A researcher comparing the means of two groups calculates the t-test for independent means and reports the following result: t(22) = -3.54, p <.01. This research study consisted of a TOTAL of ______ participants.

A study compares the means of two groups, each having N = 10. If the standard deviations in the two groups are 4.00 and 6.00, what is the value for the standard error of the difference ?

A study tests the difference between 15 ants and 15 ladybugs. In this example, the degrees of freedom is ______.

In testing the difference between two means, which of the following is implied by the alternative hypothesis (H₁) ?

A researcher comparing the means of two groups calculates the t-test for independent means and reports the following result: t(28) = 2.11, p <.05. This research study consisted of a TOTAL of ______ participants.

A researcher states the following hypotheses: H₀: μ Freshmen = μ Sophomores and H₁: μ Freshmen ≠ μ Sophomores. Assuming she collects data from 13 freshmen and 13 sophomores, what is the appropriate critical value?

A researcher states the following hypotheses: H₀: μCity1 = μCity2 and H₁: μCity1 > μCity2. Assuming she collects data from 30 people who live in city 1 and 30 people who live in city 2, what is the appropriate critical value?

In testing the difference between two sample means , the greater the difference between the two means, the more the value of the t-statistic (t) differs from ______.

A study compares the means of two groups, each having N = 10. If the standard deviations in the two groups are 3.00 and 5.00, what is the value for the standard error of the difference ?