Understanding t-test

What is the t-test used for?

• To identify outliers in a dataset.

• To determine the standard deviation of a single group.

• To determine if there is a significant difference between the test scores of Ava and Liam.

• To calculate the correlation coefficient between two variables.

Tags

CCSS.HSS.IC.B.4

What are the assumptions of the t-test?

• The data is skewed

• The sample size is small

• The groups being compared are not independent

• The assumptions of the t-test include: 1. The data is normally distributed within each group. 2. The variances of the populations being compared are equal. 3. The observations are independent of each other.

What is the difference between a one-sample t-test and a two-sample t-test?

• One-sample t-test compares a sample mean to a known value, while a two-sample t-test compares the means of two independent samples.

• One-sample t-test compares the means of two independent samples.

• Two-sample t-test compares a sample mean to a known value.

• One-sample t-test compares two independent samples.

When should Sophia use a paired t-test?

• When you have two independent groups or conditions and want to compare their means.

• When you have two related groups or conditions and want to compare their means.

• When you want to compare more than two groups or conditions.

• When you want to analyze categorical data.

Tags

CCSS.HSS.ID.A.4

Explain the concept of degrees of freedom in the t-test using a real-world scenario.

• Degrees of freedom in a t-test represent the number of independent pieces of information available to estimate the variability in the data, which is crucial for determining the appropriate critical values from the t-distribution.

• Degrees of freedom in a t-test refer to the number of participants in the study

• Degrees of freedom in a t-test are calculated by dividing the sample size by the number of groups

• Degrees of freedom in a t-test are only relevant for one-tailed tests

What is the null hypothesis in a t-test?

• The sample size is too small for the t-test.

• The t-test is not applicable in this scenario.

• There is no significant difference between the heights of students in Group A and Group B.

• The heights of students in Group A and Group B are significantly different.

What is the significance level commonly used in hypothesis testing?

• 0.01

• 0.10

• 0.05

• 0.25

Tags

CCSS.HSN.Q.A.1

What is the interpretation of the p-value in a t-test?

• The p-value in a t-test represents the probability of obtaining the observed data, or more extreme results, when the null hypothesis is true.

• The p-value determines the effect size in the t-test

• The p-value represents the sample size in the t-test

• The p-value indicates the strength of the relationship between variables in the t-test

What are the advantages of using a t-test over other statistical tests?

• Complexity, ability to compare medians of two groups, and sensitivity to normality assumptions

• Difficulty, ability to compare modes of two groups, and vulnerability to violations of independence assumptions

• Simplicity, ability to compare means of two groups, and robustness to violations of normality assumptions.

• Ease of use, ability to compare variances of two groups, and resistance to violations of homoscedasticity assumptions

What is the impact of violating the assumption of equal variances in a t-test?

• It leads to an underestimation of the standard error and an inflated Type I error rate

• It has no effect on the results of the t-test

• It results in a more accurate estimation of the population parameter

• It increases the power of the t-test