One Sample T-Test
As the name implies, this test is used when we have one data set for a sample and we need to determine whether this data set belongs to a particular population or not. The mean value for the population data must be known in this case. The formula to determine T-value, in this case, is as follows:
t = (x̄ – μ) / (σ / √n)
Where,
- t is the t-value,
- x̄ is the Sample mean,
- μ is the Population mean,
- σ is the Sample standard deviation, and
- n is the Sample size.
Steps to Calculate T Value One Sample T-Test
To perform the One Sample T-test, the steps listed below are generally followed:
Step 1: State a null hypothesis and an alternative hypothesis. The null hypothesis assumes that the sample mean and the known population mean (μ) are equal, while the other assumes that the sample mean is different from the population mean.
Step 2: Define values for the level of significance (α) and the degree of freedom (df). The degree of freedom equals (n – 1) for this case.
Step 3: Calculate the t-value using the formula stated above by putting all the known values of the sample mean (x̄), sample standard deviation (σ), the population mean (μ), and the sample size (n).
Step 4: Determine the associated p-value with the t-value using a t-distribution table.
Step 5: Compare the p-value to the level of significance. If the p-value is less than the level of significance, reject the null hypothesis and conclude that the sample mean is significantly different from the population mean. Otherwise, conclude that there is no significant difference between the sample mean and the population mean.
T-Test in Statistics: Formula, Types and Steps
T-Test is a method used in statistics to determine if there is a significant difference between the means of two groups and how they are related. In T-Test statistics, the sample data is a subset of the two groups that we use to draw conclusions about the groups as a whole.
For example, if we want to know the average weight of mangoes grown on a farm, the population would consist of all the mangoes that grew on the farm. However, it would be time-consuming to weigh each mango. Instead, we could take a sample of mangoes from trees at different locations on the farm and use their weights to make inferences about the average weight of all the mangoes grown on the farm.
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