Comparing Means 1

Question 1

What is the purpose of comparing means in experiments?

1) To calculate individual differences within a group
2) To determine if the independent variable affects the dependent variable
3) To classify data into categories
4) To measure variability within a sample

Answer 1

To determine if the independent variable affects the dependent variable

Question 2

What is the null hypothesis in a t-test comparing two group means?

1) The means are significantly different between the two groups
2) The sample means are equal
3) The population means are unequal
4) There is no variability within the samples

Answer 2

The sample means are equal

Question 3

What is the primary difference between descriptive and inferential statistics?

1) Descriptive statistics analyze variability within populations, while inferential statistics compare group means
2) Descriptive statistics summarize data from a sample, while inferential statistics generalize findings to a population
3) Descriptive statistics are only used for categorical data, while inferential statistics require continuous data
4) Descriptive statistics are used for large datasets, while inferential statistics are for small samples

Answer 3

Descriptive statistics summarize data from a sample, while inferential statistics generalize findings to a population

Question 4

What does a p-value represent in hypothesis testing?

1) The exact mean difference between two samples
2) The likelihood that the observed difference is due to chance under the null hypothesis
3) The variability within a single sample
4) The degrees of freedom used in the t-test

Answer 4

The likelihood that the observed difference is due to chance under the null hypothesis

Question 5

What is the typical threshold for statistical significance in a t-test?

1) p < .10
2) p < .01
3) p < .05
4) p ≥ .05

Answer 5

p < .05

Question 6

What does the t-statistic measure in a t-test?

1) The total variance between two groups
2) The number of standard deviations the group means are apart
3) The sum of individual scores within a group
4) The likelihood of committing a Type I error

Answer 6

The number of standard deviations the group means are apart

Question 7

What is the formula to calculate degrees of freedom (df) for an independent samples t-test?

1) df = n1 + n2
2) df = n1 - n2
3) df = (n1 + n2) - 2
4) df = n1 + n2 - 1

Answer 7

df = (n1 + n2) - 2

Question 8

What is the primary assumption of an independent samples t-test?

1) Both groups have equal means
2) The groups are related or paired
3) The data for each group is normally distributed
4) Each individual participates in both conditions

Answer 8

The data for each group is normally distributed

Question 9

What does Levene’s test assess in an independent samples t-test?

1) The normality of the data distribution
2) Whether the sample means are significantly different
3) The equality of variances between two groups
4) The effect size of the difference between means

Answer 9

The equality of variances between two groups

Question 10

What action should be taken if Levene’s test indicates unequal variances?

1) Use a non-parametric test instead of a t-test
2) Assume equal variances and proceed with the analysis
3) Apply a t-test that does not assume equal variances
4) Exclude outliers to balance the variances

Answer 10

Apply a t-test that does not assume equal variances

Question 11

What is the significance of the standard error in a t-test?

1) It measures the spread of scores within a single sample
2) It represents the standard deviation of the sampling distribution of the mean
3) It determines whether the null hypothesis is accepted or rejected
4) It indicates the reliability of the sample size

Answer 11

It represents the standard deviation of the sampling distribution of the mean

Question 12

What does it mean if p ≥ .05 in a t-test?

1) The null hypothesis is rejected
2) There is a statistically significant difference between the group means
3) The null hypothesis cannot be rejected
4) The test results are invalid

Answer 12

The null hypothesis cannot be rejected

Question 13

What type of t-test is appropriate for comparing two unrelated groups?

1) Paired samples t-test
2) Independent samples t-test
3) One-sample t-test
4) Repeated measures t-test

Answer 13

Independent samples t-test

Question 14

Which measure is most affected by sample size in a t-test?

1) Standard deviation
2) Mean difference
3) Standard error
4) Variance

Answer 14

Standard error

Question 15

Why is the independent samples t-test sometimes called a “between-groups t-test”?

1) Because it examines differences within a single group
2) Because it compares means across separate, unrelated groups
3) Because it compares changes over time in the same group
4) Because it ignores variability between groups

Answer 15

Because it compares means across separate, unrelated groups

Question 16

What does a t-statistic of 0 indicate?

1) There is no difference between the group means
2) The data violates the assumptions of the t-test
3) The variances of the groups are equal
4) The test is invalid due to insufficient sample size

Answer 16

There is no difference between the group means

Question 17

What are the two key outputs of a t-test?

1) The standard deviation and p-value
2) The t-statistic and p-value
3) The mean difference and variance ratio
4) The effect size and correlation coefficient

Answer 17

The t-statistic and p-value

Question 18

What should be reported alongside the t-statistic in results?

1) Exact p-value and degrees of freedom
2) Sample size and effect size
3) Standard deviation and test type
4) Confidence interval and critical value

Answer 18

Exact p-value and degrees of freedom

Question 19

What does a significant t-test result indicate?

1) The observed difference in sample means likely reflects a real difference in the population means
2) The null hypothesis is always true
3) Variability within groups is higher than between groups
4) The alternative hypothesis is invalid

Answer 19

The observed difference in sample means likely reflects a real difference in the population means

Question 20

What does “statistical significance” imply about practical significance?

1) Statistical significance guarantees practical importance
2) Statistical significance does not necessarily indicate practical relevance
3) Practical significance is always larger than statistical significance
4) Statistical significance is determined by practical implications

Answer 20

Statistical significance does not necessarily indicate practical relevance