Estimate ranges, run z, t, and proportion tests fast. Review p-values, margins, and decisions instantly. Turn sample evidence into confident statistical conclusions now easily.
| Mode | Main Inputs | Null Value | Confidence | Alpha |
|---|---|---|---|---|
| Mean with known deviation | x̄ = 52.4, σ = 8, n = 64 | μ₀ = 50 | 95% | 0.05 |
| Mean with unknown deviation | x̄ = 18.7, s = 4.2, n = 25 | μ₀ = 20 | 95% | 0.05 |
| Population proportion | x = 146, n = 250 | p₀ = 0.50 | 95% | 0.05 |
Standard error = σ / √n
Critical value = zα/2
Confidence interval = x̄ ± zα/2 × standard error
Standard error = s / √n
Critical value = tα/2, n-1
Confidence interval = x̄ ± tα/2, n-1 × standard error
Sample proportion = x / n
Standard error = √[ p̂(1 − p̂) / n ]
Confidence interval = p̂ ± zα/2 × standard error
Mean z test: z = (x̄ − μ₀) / (σ / √n)
Mean t test: t = (x̄ − μ₀) / (s / √n)
Proportion z test: z = (p̂ − p₀) / √[ p₀(1 − p₀) / n ]
The p-value depends on the chosen alternative hypothesis.
A confidence interval and hypothesis testing calculator helps you make stronger numerical decisions. It turns sample data into useful statistical evidence. The interval shows a plausible range. The test checks whether a claim is supported. Together, they improve clarity in maths, research, business, and academic work.
A confidence interval estimates an unknown population value. It combines the sample estimate, the standard error, and a critical value. A narrower interval suggests more precision. A wider interval suggests more uncertainty. Larger samples often reduce the margin of error. Higher confidence levels usually increase the interval width.
Hypothesis testing compares your observed sample result with a null claim. The calculator reports a z statistic or t statistic. It also reports a p-value. A small p-value suggests the sample is unusual under the null hypothesis. When the p-value is smaller than alpha, the null hypothesis is rejected.
Use the mean known deviation option when the population deviation is available. Use the mean unknown deviation option when only the sample deviation is known. Use the proportion mode for binary outcomes, such as yes or no results. Choosing the correct model improves interpretation and keeps results relevant.
Always read the interval and test result together. If a null value falls outside a two sided confidence interval, rejection often follows at a matching significance level. This makes the calculator practical for teaching, revision, and real analysis. It supports clear explanations, faster checks, and better statistical reasoning.
A confidence interval gives a plausible range for the unknown population parameter. It is built from the sample estimate, variability, and chosen confidence level.
A z test uses a known population deviation or a large sample approximation. A t test is used when the population deviation is unknown and estimated from the sample.
The p-value measures how unusual your sample result would be if the null hypothesis were true. Smaller values suggest stronger evidence against the null claim.
The confidence level controls the interval estimate. Alpha controls the testing threshold. They are related, but they serve different reporting purposes in this calculator.
Yes. The calculator supports two sided, left tailed, and right tailed alternatives. Select the option that matches your research claim before calculating.
Use the proportion mode when your data counts successes out of total trials. Common examples include pass rates, click rates, approval rates, and defect rates.
A larger sample usually reduces the standard error. That often narrows the confidence interval and can make the hypothesis test more sensitive to real differences.
Yes. After a successful calculation, use the CSV button for spreadsheet style output or the PDF button for a simple report file.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.