# Tell me about Student’s t-test!

1. What is the Student’s t-test used for?

The Student’s t-test is a statistical test used to compare the means of two groups or samples.

1. What are the assumptions of the Student’s t-test?

The assumptions of the Student’s t-test are:

• Normality of the data
• Homogeneity of variances
• Independence of observations
1. What is the difference between a one-tailed and a two-tailed t-test?

In a one-tailed t-test, the null hypothesis is tested against a one-sided alternative hypothesis. In a two-tailed t-test, the null hypothesis is tested against a two-sided alternative hypothesis.

1. What is the formula for the Student’s t-test?

The formula for the Student’s t-test is: t = (x1 – x2) / (s * sqrt(1/n1 + 1/n2)) where x1 and x2 are the sample means, s is the pooled standard deviation, n1 and n2 are the sample sizes.

1. What is the null hypothesis for the Student’s t-test?

The null hypothesis for the Student’s t-test is that there is no significant difference between the means of the two groups or samples.

1. What is the alternative hypothesis for the Student’s t-test?

The alternative hypothesis for the Student’s t-test is that there is a significant difference between the means of the two groups or samples.

1. What is the significance level for the Student’s t-test?

The significance level for the Student’s t-test is typically set to 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is true.

1. What is the degrees of freedom for the Student’s t-test?

The degrees of freedom for the Student’s t-test is equal to (n1 + n2 – 2), where n1 and n2 are the sample sizes.

1. What is a paired t-test?

A paired t-test is a type of t-test used to compare the means of two related groups or samples, such as before and after measurements or matched pairs.

1. What is an independent t-test?

An independent t-test is a type of t-test used to compare the means of two independent groups or samples.

1. What is a pooled variance?

The pooled variance is a weighted average of the variances of two samples used in the formula for the pooled standard deviation in the independent t-test.

1. What is the formula for the pooled variance?

The formula for the pooled variance is: s^2 = [(n1-1)s1^2 + (n2-1)s2^2] / (n1 + n2 – 2) where s1^2 and s2^2 are the variances of the two samples, and n1 and n2 are the sample sizes.

1. What is a type I error in the context of the t-test?

A type I error in the context of the t-test is the rejection of the null hypothesis when it is actually true.

1. What is a type II error in the context of the t-test?

A type II error in the context of the t-test is the failure to reject the null hypothesis when it is actually false.

1. What is the power of a t-test?

The power of a t-test is the probability of correctly rejecting the null hypothesis when it is false.

1. How is the power of a t-test calculated?

The power of a t-test is calculated using the formula: Power = 1 – beta, where beta is the probability of a type II error.

1. What is effect size in the context of the t-test?

Effect size in the context of the t-test is a measure of the magnitude