AS and A Level Biology 16 Views 1 Answers
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Sourav PanNovember 1, 2024

Use the t-test to compare the means of two different samples (the formula for the t-test will be provided, as shown in the Mathematical requirements)

Use the t-test to compare the means of two different samples (the formula for the t-test will be provided, as shown in the Mathematical requirements)

Sourav Pan
Sourav PanNovember 1, 2024

Answered

To perform a t-test to compare the means of two samples, we follow these steps:

Formula for the T-test

Given two samples with means X1ˉ\bar{X_1} and X2ˉ\bar{X_2}, sample sizes n1n_1 and n2n_2, and variances s12s_1^2 and s22s_2^2, the formula for the t-test is:

t = \frac{\bar{X_1} - \bar{X_2}}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}

where:

  • X1ˉ\bar{X_1} and X2ˉ\bar{X_2} are the means of the two samples,
  • s12s_1^2 and s22s_2^2 are the variances of the two samples,
  • n1n_1 and n2n_2 are the sample sizes.

Steps for Performing the T-Test

  1. Calculate the Means \bar{X_1} and \(\bar{X_2} of each sample.
  2. Calculate the Variances s_1^2 and \(s_2^2 of each sample.
  3. Plug values into the formula to calculate the t-value.
  4. Compare the t-value to a critical value from a t-distribution table (based on the chosen significance level, e.g., 0.05) and the degrees of freedom.

The degrees of freedom (df) can be approximated as:

df = \min(n_1 - 1, n_2 - 1)

If you have specific data for two samples, I can calculate the t-test result for you. Just provide the values, and I’ll walk you through the process.

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