It is imperative for a statistician to understand the concept of t-test as it holds significant importance while drawing conclusive evidence about whether or not two data sets have statistics that are not very different. T = ( x̄ 1 – x̄ 2) / √ Relevance and Use of t-Test Formula Step 4: Finally, the formula for a two-sample t-test can be derived using observed sample means (step 1), sample standard deviations (step 2) and sample sizes (step 3) as shown below. Step 3: Next, determine the size of the two samples, which are denoted by and. Step 2: Next, determine the standard deviation of the two samples, which are denoted by and. Step 1: Firstly, determine the observed sample mean of the two samples under consideration. The formula for the two-sample t-test can be derived by using the following steps: Step 4: Finally, the formula for a one-sample t-test can be derived using the observed sample mean (step 1), the theoretical population means (step 1), sample standard deviation (step 2) and sample size (step 3), as shown below. Step 3: Next, determine the sample size, which is the number of data points in the sample. Step 2: Next, determine the standard deviation of the sample, and it is denoted by s. The sample mean and population mean is denoted by and μ, respectively. Step 1: Firstly, determine the observed sample mean, and the theoretical population means specified. The formula for one-sample t-test can be derived by using the following steps: So, the hypothesis that the statistics of the two samples are significantly different can’t be rejected. Therefore, the absolute t-test value is 4.31, which is greater than the critical value (3.03) at a 99.5% confidence interval with a degree of freedom of 30. T-Test value is calculated using the formula given below Determine if the sample’s statistics are different at a 99.5% confidence interval. The two samples have means of 10 and 12, standard deviations of 1.2 and 1.4, and sample sizes of 17 and 15.
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Let us take the example of two samples to illustrate the concept of a two-sample t-test.