Hypothesis Test Calculator
Standard deviation and sample size must be greater than 0
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What is a Hypothesis Test Calculator?
A hypothesis test calculator performs statistical hypothesis testing to determine whether sample data provides sufficient evidence to reject a null hypothesis in favor of an alternative hypothesis.
This calculator performs one-sample Z-tests, calculating test statistics, p-values, and critical values to help you make statistical decisions based on your data.
Key Applications:
- Quality control and manufacturing
- Medical and pharmaceutical research
- Market research and A/B testing
- Academic research and studies
- Business decision making
How It Works
Set Hypotheses
Define H₀ and H₁
Enter Data
Input sample statistics
Calculate
Compute test statistic
Compare
Check p-value vs α
Z-Test Formula
z = (x̄ - μ) / (σ / √n)
Where x̄ is sample mean, μ is population mean
Decision Rule
If p-value < α, reject H₀
Otherwise, fail to reject H₀
Common Examples
Quality Control
Medical Research
A/B Testing
Calculation Table
| Test Type | Formula | When to Use | Assumptions |
|---|---|---|---|
| One-Sample Z-Test | z = (x̄ - μ) / (σ / √n) | Known population σ | Normal distribution, σ known |
| Critical Value (α=0.05) | ±1.96 (two-tailed) | Decision boundary | Standard normal distribution |
| P-Value | P(Z ≥ |z|) | Probability of result | Under null hypothesis |
| Decision Rule | p < α → Reject H₀ | Statistical decision | Significance level α |
Frequently Asked Questions
What is hypothesis testing?
Hypothesis testing is a statistical method used to make decisions about population parameters based on sample data. It involves testing a null hypothesis (H₀) against an alternative hypothesis (H₁).
What's the difference between one-tailed and two-tailed tests?
A two-tailed test checks if the parameter is significantly different from the hypothesized value (≠). One-tailed tests check if it's significantly greater than (>) or less than (<) the hypothesized value.
What is a p-value?
The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true. If p-value < α, we reject the null hypothesis.
How do I choose the significance level?
Common significance levels are 0.05 (5%), 0.01 (1%), and 0.10 (10%). Choose 0.05 for general research, 0.01 for more stringent requirements, or 0.10 for exploratory analysis.
When should I use a Z-test vs T-test?
Use a Z-test when the population standard deviation is known and sample size is large (n ≥ 30). Use a T-test when the population standard deviation is unknown or sample size is small.
What does "fail to reject H₀" mean?
"Fail to reject H₀" means there's insufficient evidence to conclude the alternative hypothesis is true. It doesn't prove H₀ is true, just that we don't have enough evidence against it.