## Single Sample Test Statistic Calculator -

The single sample test statistic calculator or simply known as the t-test calculator is used for comparison of the mean acquired from a single sample to the scores of a known/hypothetical mean population. For example, this calculator can easily be used for calculation of the mean for Diastolic Blood Pressure of a particular patient group.

## Requirements for Test Statistic Calculator

• Normally Distributed Data
• Measurement Scale needs to be ratio or interval
• Randomized Sample obtained from a defined population

## How to calculate Test-Statistic?

Test Statistic Calculator designed for 1-Population Mean is used when there is a numerical variable with just a single population or a group being studied. Say, for example, an economist named Julia Williams believes that the students who tend to go to work while spending the rest time at college, pay a mere \$15 per day for food. The variable here is money, which is numerical with the population being students that go to work and college. So, if you are wondering how to calculate test-statistic, here is a well-elaborated process. For this example, the overall null hypothesis stands

H0= μ= \$15

Here the symbol 'μ' represents the dollars amount or average money spent by working students per day over food. Here, the economist claims that this is the average money spent per day totaling a \$15.

### To this, the substitute hypothesis is

Ha (μ > 15, μ < 15, or μ ≠ 15)
In this particular example, we can say that the average Ha equals \$20 per day. So, in this case, the substitute hypothesis states that the working class students have an average expenditure rate of \$20 per day for food as opposed to the \$15 confirmed by an economist.
So, from this example, we can estimate the test statistic value for 1 population means using the formula:
Z= (x - μ0)/(σ/√n)
This formula can change according to the population value being tested. This is why; the use of a test statistic calculator is a must. The standardized test statistic calculator allows for easy extraction of values using pre-set formulas. Now, all you are required to do is enter required values of all parameters, and the calculator almost instantly produces the results.

## What does the T-test calculator do?

This particular calculator conducts a complete 1-sample-based t-test. The calculation process requires parameters such as:

• Sample Mean
• Sample Size
• Hypothesized Mean
• Sample Standard Deviation

The results calculated thus include the value of the T-Statistic, Degrees of Freedom, Two-Tailed Hypotheses (Non-Directional), One-Tailed Hypotheses (Directional), Critical T-Values, One-Tailed Probability Values, and Two-Tailed Probability Values.

## What is the meaning of Standardized Test Statistic Calculator?

The standardized test statistic calculator is an easy way for anyone to compare the results with a 'Normal' population. The T-Scores and Z-Scores are comparatively similar. However, the T-Distribution here is a bit shorter & fatter as compared to normal distribution. They tend to do similar things. In the elementary statistics, one shall start with the use of z-score. As you go ahead, you can use the T-Scores for mean calculation of the small populations. Generally, you need to know that standard deviation for the population with a sample size that needs to be more than 30 for one to use the z-score. Else, you can go with T-score.

### Parameters for T-Test

#### Sample Size:

When wondering how to find the test statistic, you need to keep in mind certain essential parameters. The sample size is total sample numbers that are randomly drawn from the population. The bigger the size of your sample, higher is the chances of certainty for your estimation reflecting a certain population. Picking the right sample size comes as a crucial aspect, especially when designing the survey or study.

#### P-Value:

P-value is actually the probability confirming the difference between Sample Means to be as big as the observable number. This is under an assumption that population means tend to be equal. In short, the lower your p-value, the bigger difference between the actual sample Mean and the observed sample mean. So, the smaller your p-value, stronger is the evidence for two populations with variable means. This is a crucial parameter when searching for ways that enunciate how to find the test statistic.

#### Sample Mean:

The sample mean in statistics is the guesswork for what your true mean for the population can be. Based on this, the data is calculated for T-test or test statistics.

#### Sample Standard Deviation:

When going for a standardized test statistic, the Sample Standard Deviation deals with a certain data set. However, if one wants to determine the standard deviation for a large population, one can use the sample standard deviation.