Test Hypothesis Statistics Calculator

Calculator Form

Test type

Alternative direction

Alpha level

Null value

Use 0 for most differences. Use p0 for one proportion.

Sample mean 1

Standard deviation 1

Sample size 1

Sample mean 2

Standard deviation 2

Sample size 2

Successes 1

Trials 1

Successes 2

Trials 2

Mean paired difference

Standard deviation of differences

Number of pairs

Example Data Table

Test	Sample Inputs	Null Value	Tail	Use Case
One sample t test	x-bar = 72, s = 10, n = 30	70	Two tailed	Compare one sample average with a claimed mean.
Two proportions z test	56/100 versus 45/95	0	Right tailed	Compare two independent success rates.
Paired t test	d-bar = 4.2, sd = 6.5, n = 20	0	Two tailed	Compare before and after paired results.

Formula Used

The calculator selects a formula from the chosen test type.

One mean z test: z = (xbar - mu0) / (sigma / sqrt(n))
One mean t test: t = (xbar - mu0) / (s / sqrt(n))
One proportion z test: z = (phat - p0) / sqrt(p0(1 - p0) / n)
Two means z test: z = ((xbar1 - xbar2) - D0) / sqrt(sigma1^2/n1 + sigma2^2/n2)
Welch two means t test: t = ((xbar1 - xbar2) - D0) / sqrt(s1^2/n1 + s2^2/n2)
Two proportions z test: z = ((p1hat - p2hat) - D0) / sqrt(ppooled(1 - ppooled)(1/n1 + 1/n2))
Paired t test: t = (dbar - D0) / (sd / sqrt(n))

The p value is computed from the selected tail direction.

How to Use This Calculator

Select the hypothesis test that matches your data.
Choose the alternative direction.
Enter alpha, such as 0.05.
Enter the null value for the claim.
Fill only the fields required by the selected test.
Press Calculate to view the result above the form.
Use CSV or PDF to save your result.

Understanding Hypothesis Testing

What the Test Does

Hypothesis testing helps you judge a claim with sample evidence. It starts with a null hypothesis. The null usually says no change, no difference, or a stated value. The alternative says the effect is different, greater, or smaller. This calculator supports common mean and proportion tests. It can handle one sample, two independent samples, and paired samples. It also supports left tailed, right tailed, and two tailed decisions.

How Evidence Is Measured

A test statistic measures how far the sample estimate sits from the null value. A large absolute statistic often means stronger evidence against the null. The p value gives the probability of seeing results this extreme when the null is true. A smaller p value gives stronger evidence. The alpha level is your chosen cutoff. Common choices are 0.05, 0.01, and 0.10. When the p value is less than or equal to alpha, reject the null hypothesis.

Choosing the Correct Method

Choosing the correct test matters. Use a one sample mean test for one average. Use the z version when the population standard deviation is known. Use the t version when you only know the sample standard deviation. Use a one proportion test for one rate or percentage. Use two sample tests when comparing two independent groups. Use the paired t test when each observation has a natural before and after pair.

Practical Reporting Tips

This tool is useful for class work, reports, quality checks, and research planning. It shows the formula path, standard error, statistic, p value, and decision. You can export the result as CSV or PDF. The example table shows typical inputs. Always check assumptions before reporting. Samples should be random when possible. Groups should be independent unless you choose the paired test. Counts in proportion tests should be large enough for a normal approximation.

Careful Interpretation

Hypothesis testing does not prove a claim forever. It only summarizes evidence from the available sample. A non rejection does not prove the null is true. It means the sample did not give enough evidence against it. Report the test type, alternative direction, statistic, degrees of freedom when used, p value, alpha level, and conclusion. Clear reporting keeps your analysis transparent and easy to review. Use practical context, not only numbers, when explaining the final finding to readers.

FAQs

What is a null hypothesis?

It is the starting claim tested by the sample. It often says there is no difference, no change, or a stated population value.

What is an alternative hypothesis?

It is the claim tested against the null. It can be two tailed, left tailed, or right tailed.

What does the p value mean?

The p value measures how unusual the sample result is under the null hypothesis. Smaller values give stronger evidence against the null.

When should I use a t test?

Use a t test when working with means and sample standard deviations. It is common when the population standard deviation is unknown.

When should I use a z test?

Use a z test for proportions or for means when the population standard deviation is known. Large samples also support z methods.

What alpha value should I enter?

Many reports use 0.05. Stricter tests may use 0.01. Exploratory work may use 0.10 when justified.

Does rejection prove the alternative is true?

No. Rejection means the sample evidence is strong enough against the null at your selected alpha level.

Can I download the result?

Yes. Use the CSV button for spreadsheet records. Use the PDF button for a simple printable report.