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# One Sample T-test Calculator + Online Solver With Free Steps

The online **One Sample T-test Calculator** is a calculator that compares the mean of a sample data to a known value.

The** One Sample T-test Calculator** is a powerful tool for determining the relationship between sample data and a known data set.

## What Is a One Sample T-test Calculator?

**A One Sample T-test Calculator is an online calculator that helps you perform a test that allows you to determine the relationship between the sample data and the known data.**

The **One Sample T-test Calculator** needs four inputs to work: the t-test or hypothesized mean, the sample mean, the sample standard deviation, and the size of the sample.

After inputting these values in the **One Sample T-test Calculator**, we can easily compare the means.

## How To Use a One Sample T-test Calculator?

You can use the calculator by plugging the values in their respective boxes and clicking the “Submit” button to get the desired results.

The detailed step-by-step instructions on how to use the **One Sample T-test Calculator** can be found below:

### Step 1

In the initial step, we enter the **t-test** or** hypothesized mean** value into the **One Sample T-test Calculator.**

### Step 2

After we enter the t-test value, we enter the **sample mean** value into our calculator.

### Step 3

After entering the sample mean value, we enter the **sample standard deviation** in the **One Sample T-test Calculator**.

### Step 4

After inputting the sample standard deviation, we enter the last input value, **the sample size**, in the **One Sample T-test Calculator**.

### Step 5

Finally, after adding all the values to the calculator, you click on the “**Submit” **button present on the calculator. The **One Sample T-test Calculator **quickly displays the relationship between the sampled data mean and known data. The calculator also plots a **distribution curve** representing the results.

## How Does a One Sample T-test Calculator Work?

The **One Sample T-test Calculator** works by taking in the input values and comparing the sample data with the known sample. The **One Sample T-test Calculator** uses the following equation to compute the t value:

\[ t = \frac{\bar{x}-\mu}{\frac{S}{\sqrt{n}}} \]

Where:

x= the calculated mean.

$\mu$ = hypothetical mean.

S = standard deviation.

n= number of samples.

## What Is a One Sample T-test?

A **one-sample t-test **is a test that compares your sample data’s mean to a given value. For instance, you might be curious about how your **sample mean** compares to the population mean. When the population **standard deviation **is unknown or have a small **sample size**, you should use a **one-sample t-test**.

To implement the one-sample t-test, you need to make sure the following assumptions are valid:

- The variable under investigation should be either an interval or ratio variable.
- Observations in the sample should be independent of one another.
- A variable under investigation should be roughly
**normally distributed**. You can test this assumption by making a histogram and visually inspecting the distribution to see if it has a “bell shape.” - There should be no outliers in the variable under investigation. Create a boxplot and visually inspect for outliers to test this premise.

## Solved Examples

The **One Sample T-test Calculator** can instantly perform a one-sample t-test. You only need to provide the calculator with the input values.

Here are some examples solved using the **One Sample T-test Calculator**:

### Example 1

While conducting his research, a student comes across the following values:

Hypothesized mean = 90

Sample Mean = 85

Sample Standard Deviation = 3

Sample Size = 15

The student must find the relationship between the sample mean and the known data value.

Use the **One Sample T-test Calculator** to find this relationship

### Solution

We can easily find the t-test value using the **One Sample T-test Calculator**. First, we input the hypothesized mean value into the calculator; the hypothesized value mean 90. We then enter the sample mean value in the **One Sample T-test Calculator**; the **sample means** the value is 85. Now we enter the sample standard deviation value in the calculator; the value is 3. Finally, we enter the sample size into the **One Sample T-test Calculator**; the sample size value is 15.

After adding all the values in the **One Sample T-test Calculator**, we click the **“Submit**” button. The results appear in a new window.

The following results are from the **One Sample T-test Calculator**:

Null Hypothesis:

\[ \mu = 90 \]

Alternative Hypothesis:

\[ \mu < 90 \]

Test Statistic:

\[ -\sqrt{15} \approx -3.87298 \]

Degrees of freedom:

14

P Value:

\[ 8.446 \times 10^{-4} \]

Sampling distribution of test statistics under the null hypothesis:

Test Conclusions:

The null hypothesis **is rejected** at a 1**% significance level**.

The null hypothesis **is rejected** at a **5% significance level**.

The null hypothesis **is rejected** at a **10% significance level**.

### Example 2

Consider the following values:

Hypothesized mean = 302

Sample Mean = 300

Sample Standard Deviation = 18.5

Sample Size = 40

Use the **One Sample T-test Calculator** to find the relationship between the sampled and known data.

### Solution

We can quickly calculate the t-test value using the **One Sample T-test Calculator**. First, we enter the **hypothesized mean number** into the calculator; the hypothesized mean value is 302. We then enter the **sample mean value** of 300 into the **One Sample T-test Calculator**. Now we enter the **sample standard deviation** value into the calculator; the value is 18.5. Finally, we enter the sample size into the **One Sample T-test Calculator**; the sample size value is 40.

We click the **“Submit”** button after inputting all values into the **One Sample T-test Calculator**. The outcomes appear in a separate window.

The **One Sample T-test Calculator** gives the following results:

Null Hypothesis:

\[ \mu = 302 \]

Alternative Hypothesis:

\[ \mu < 302 \]

Test Statistic:

-0.683736

Degrees of freedom:

39

P Value:

0.249

Sampling distribution of test statistics under the null hypothesis:

Test Conclusions:

The null hypothesis **is not rejected** at a **1% significance level**.

The null hypothesis **is not rejected** at a **5% significance level**.

The null hypothesis **is not rejected** at a **10% significance level**.

*All images/Graphs are created using GeoGebra.*