Choose the method, enter the values into the test statistic calculator, and click on the “Calculate” button to calculate the statistical value for hypothesis evaluation.
This test statistic calculator helps to find the static value for hypothesis testing. The calculated test value shows if there’s enough evidence to reject a null hypothesis. Also, this calculator performs calculations of either for one population mean, comparing two means, single population proportion, and two population proportions.
Our tool is highly useful in various fields like research, experimentation, quality control, and data analysis.
A test statistic is a numerical value obtained from the sample data set. It summarizes the differences between what you observe within your sample and what would be expected if a hypothesis were true.
The t-test statistic also shows how closely your data matches the predicted distribution among the sample tests you perform.
Test statistics for a single population mean is calculated when a variable is numeric and involves one population or a group.
x̄ - µ0 σ / √n
Where:
Example:
Suppose we want to test if the average height of adult males in a city is 70 inches. We take a sample of 25 adult males and find the sample mean height to be 71 inches with a sample standard deviation of 3 inches. We use a significance level of 0.05.
t = 70 - 71 3√25
t = 1 0.6
t = 1.67
This test is applied when the numeric value is compared across the various populations or groups. To compute the resulting t statistic, two distinct random samples must be chosen, one from each population.
\(\frac{√x̄ - √ȳ}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}\)
Where:
Example:
Suppose we want to test if there is a difference in average test scores between two schools. We take a sample of 30 students from school A with an average score of 85 and a standard deviation of 5, and a sample of 35 students from school B with an average score of 82 and a standard deviation of 6.
t = 85 - 82 √5 2 / 30 + 6 2 / 35
t = 3 √ 25/30 + 36/35
t = 3 √0.833 + 1.029
t = 3 √1.862
t = 2.20
This test is used to determine if a single population's proportion differs from a specified standard. The t statistic calculator works for a population proportion when dealing with data by having a limit of P₀ because proportions represent parts of a whole and cannot logically exceed the total or be negative.
\(\frac{\hat{p}-p_{0}}{\sqrt{\frac{p_{0}(1-p_{0})}{n}}}\)
Where:
Example:
Suppose we want to test if the proportion of left-handed people in a population is 10%. We take a sample of 100 people and find that 8 are left-handed. We use a significance level of 0.05.
= P̂ - P₀ √0.10 (1 - 0.10)/100
= 0.08 - 0.10 √0.10 (1 - 0.10)/100
= -0.02 √0.10 (0.9)/100
= -0.02 √0.009
= -0.02 0.03
= −0.67
This test identifies the difference in proportions between two independent groups to assess their significance.
\(\frac{\hat{p}_{1}-\hat{p}_{2}}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}\)
Where:
Example:
Suppose we want to test if the proportion of smokers is different between two cities. We take a sample of 150 people from City A and find that 30 are smokers, and a sample of 200 people from City B and find that 50 are smokers.
Calculation:
= 0.20 - 0.25 √0.229 (1 - 0.229) (1 / 150 + 1/200)
= -0.05 √0.229 (0.771) (1 / 150 + 1 / 200)
= -0.05 √0.176 (1/150 + 1/200)
= -0.05 √0.176 (0.0113)
= -0.05 √0.002
= -0.05 0.045
= −1.11
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