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What's t.test?

Mar 5, 2024

What's t.test?

Solution by Steps

step 1

Understand the purpose of a t-test: A t-test is a statistical test used to compare the means of two groups or to compare a sample mean to a known value when the population variance is unknown

step 2

Identify the type of t-test: There are different types of t-tests, including the one-sample t-test, independent two-sample t-test, and paired sample t-test. The choice depends on the experimental design and data

step 3

Formulate the null hypothesis (

H_0

) and alternative hypothesis (

H_a

): The null hypothesis typically states that there is no effect or no difference, while the alternative hypothesis states that there is an effect or a difference

step 4

Calculate the t-statistic: The t-statistic is calculated using the sample data. For a one-sample t-test, the formula is:

t = \frac{\bar{x} - \mu}{s / \sqrt{n}}

where

\bar{x}

is the sample mean,

\mu

is the population mean,

s

is the sample standard deviation, and

n

is the sample size

step 5

Determine the degrees of freedom (df): For a one-sample t-test,

df = n - 1

. For an independent two-sample t-test,

df

is calculated based on the sample sizes and variances of the two groups

step 6

Find the critical value(s) and compare with the t-statistic: Using the degrees of freedom and the desired significance level (commonly 0.05), find the critical value(s) from the t-distribution table. Compare the calculated t-statistic to the critical value(s) to determine if the null hypothesis can be rejected

step 7

Interpret the results: If the t-statistic is greater than the critical value (in absolute terms) and the p-value is less than the significance level, reject the null hypothesis. Otherwise, do not reject the null hypothesis

Answer

The t-test is a method for testing whether there is a significant difference between means or whether a sample mean significantly differs from a known value, based on the t-distribution.

Key Concept

t-test

Explanation

A t-test is used to determine if there are significant differences between the means of two groups or between a sample mean and a known population mean, especially when the population variance is unknown. It involves calculating a t-statistic and comparing it to a critical value from the t-distribution.

What is the formula for calculating the t-test statistic?

Solution by Steps

step 1

Identify the sample mean (

\bar{x}

), population mean (

\mu

), sample standard deviation (

s

), and sample size (

n

)

step 2

Use the formula for the t-test statistic for a single sample, which is:

t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}

step 3

Calculate the t-test statistic by substituting the values obtained in step 1 into the formula from step 2

Answer

The t-test statistic is calculated using the formula

t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}

Key Concept

t-test statistic calculation

Explanation

The t-test statistic is a ratio that compares the difference between the sample mean and the population mean to the standard error of the mean. It is used to determine if there are significant differences between the sample mean and the population mean.

◊What is the critical value for determining significance in a t-test?

t = \frac{\bar{x} - \mu}{s/\sqrt{n}}

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