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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:

Figure 1

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:

Figure 2

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.

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