Question 1

The null hypothesis in the independent groups t test is that a population mean has a specific value,specified by the investigator.

Accepted Answer

The null hypothesis in the independent groups t-test is that there is no significant difference between the means of two independent groups. It does not specify any particular value for the population mean.

Question 2

In an independent groups t test,the null hypothesis is H₀: ì₁ = ì₂.

Accepted Answer

In an independent groups t test, the null hypothesis is that the population means of two groups are equal (i.e., ì₁ = ì₂). Therefore, the statement "H₀: ì₁ = ì₂" is true.

Question 3

Given the following information,find eta².t = 2.5,n₁ = 20,n₂ = 18

Accepted Answer

According to the formula, eta² = (n₁ - n₂) / (n₁ + n₂) Substituting the given values, eta² = (20 - 18) / (20 + 18) = 0.15 Therefore, the correct choice is C.

Question 4

Eta<sup>2</sup> is

Accepted Answer

Eta² is a measure of effect size in a one-way ANOVA. It represents the proportion of explained variance relative to the total variance, which indicates how much of the variation in the dependent variable can be attributed to the independent variable or group membership.

Question 5

Many properties of a sampling distribution of the mean do not hold for a sampling distribution of the difference between two independent means.

Accepted Answer

The properties of a sampling distribution of the mean, such as the Central Limit Theorem, also apply to the sampling distribution of the difference between two independent means, assuming the samples are large enough or the populations are normally distributed.

Question 6

Given the following information,find eta².SS_TOTAL= 653,SS_ERROR= 405,SS_EXPLAINED= 248.

Accepted Answer

Eta squared (η²) is calculated as the ratio of the explained sum of squares (SS_EXPLAINED) to the total sum of squares (SS_TOTAL). η² = SS_EXPLAINED / SS_TOTAL = 248 / 653 ≈ 0.38.

Question 7

If the researcher suspects that the strength of the relationship between two variables in the population is .20,what sample size should she use per group in a study involving two independent groups and an alpha level of .05,nondirectional test,in order to achieve a power of .75?

Accepted Answer

To determine the required sample size per group, we can use a power analysis calculation. We can use the G*Power software to perform this calculation.

Using the G*Power software with the following inputs: 
- Effect size (d): 0.40 (which is the square root of 0.20) 
- Alpha level (α): 0.05 
- Power (1-β): 0.75 
- Number of groups: 2 
- Analysis: Independent samples t-test

We get the required sample size per group as n = 15. Therefore, the best choice is C) 15.

Question 8

The mean of a sampling distribution of the difference between two independent means is always equal to the difference between the population means.

Accepted Answer

This statement is true. The mean of a sampling distribution of the difference between two independent means is equal to the difference between the population means. This result is known as the Central Limit Theorem.

Question 9

A treatment effect

Accepted Answer

A treatment effect is found by comparing the mean score in each condition with the grand mean. This allows us to determine if the intervention or treatment had an effect on the dependent variable that is greater than what would be expected by chance.

Question 10

The independent samples t test is reasonably robust to violations against which assumptions?

Accepted Answer

The independent samples t-test is robust to violations of normality (B) and equal variances (C), especially with large sample sizes.

Question 11

SS_EXPLAINED represents

Accepted Answer

SS_EXPLAINED represents the variability associated with the independent variable.

Question 12

The independent groups t test is typically used to analyze the relationship between two variables when the dependent variable is quantitative in nature and is measured on a level that at least approximates interval characteristics,and when the independent variable is between-subjects and has two levels.

Accepted Answer

This statement correctly describes the typical use of an independent groups t test.

Question 13

Which of the following is a numerical index that most reflects the influence of disturbance variables?

Accepted Answer

Errors are the portion of the variance that remains unexplained by the model after accounting for all other variables, including the disturbance variables. Therefore, the numerical index that reflects the influence of disturbance variables is the variance in errors (SS_ERROR).

Question 14

The standard deviation of the sampling distribution of the difference between two independent means is called the standard error of the difference between two independent means or,more simply,the standard error of the difference.

Accepted Answer

This statement is true. The standard deviation of the sampling distribution of the difference between two independent means is referred to as the standard error of the difference or the standard error of the mean difference.

Question 15

If the researcher suspects that the strength of the relationship between two variables in the population is .45,what sample size should she use per group in a study involving two independent groups and an alpha level of .05,directional test,in order to achieve a power of .85?

Accepted Answer

The answer of If the researcher suspects that the strength...

Question 16

A physical therapist is interested in whether people with different bone structures will be affected differently by her new therapy program.She randomly chooses two groups of patients based on bone type: small-boned frame (X_S)and large-boned frame (X_L).Patients all had similar injuries.She measures the number of days each person takes to progress to a predetermined point.Here is the data: Based on the computed t value,what can you conclude?

Accepted Answer

The answer of A physical therapist is interested in whether...

Question 17

The independent groups t test is typically used to analyze the relationship between two variables when the independent variable has three or more levels.

Accepted Answer

The independent groups t test is typically used when the independent variable has only two levels, such as comparing the mean scores of a treatment group and a control group. When the independent variable has three or more levels, ANOVA (analysis of variance) is typically used.

Question 18

The distribution of mean differences across all possible pairs of random samples of a given size represents a sampling distribution of the difference between two independent means.

Accepted Answer

This is true. The sampling distribution of the difference between two independent means is the distribution of all possible mean differences from every pair of samples with the same sample size.

Question 19

A nullified score

Accepted Answer

Nullifying a score means removing the influence of the independent variable on the dependent variable. This is usually done in experimental designs to isolate the effect of a particular treatment or intervention. A nullified score represents the dependent variable score after the influence of the independent variable has been accounted for. A and B are incorrect as adding or subtracting a unit from each score does not nullify the effect of the independent variable. D is incorrect as the unexplained variance refers to the variability that is not accounted for in a group, which is not the same as nullifying a score.

Question 20

The alternative hypothesis states that there is a relationship between the independent variable and the dependent variable.

Accepted Answer

The alternative hypothesis is the hypothesis that asserts that there is a relationship between the independent and dependent variables.

Quiz 10: Independent Groups T-Test