Null Hypothesis Calculator

Step-by-Step Guide to Using the Null Hypothesis Calculator

Step 1: Understand the Purpose of the Calculator

This Null Hypothesis Calculator is designed to help you determine whether to reject or fail to reject a null hypothesis in a statistical test. By inputting some of your sample data and selecting your desired significance level, this tool will calculate the t-statistic, degrees of freedom, p-value, and critical value to inform your decision.

Step 2: Enter Your Input Values

• Sample Mean (x̄): Enter the mean of your sample. This is a required field, and the value should be between -1,000,000 and 1,000,000, rounded to four decimal places.
• Hypothesized Population Mean (μ₀): Enter the population mean you are testing against. This is also required and should fall within the same range as the sample mean.
• Sample Standard Deviation (s): Provide the standard deviation of your sample. The standard deviation must be a positive number, between 0 and 1,000,000, rounded to four decimal places.
• Sample Size (n): Enter the number of observations in your sample. The sample size must be at least 2 and can go up to 1,000,000, entered as a whole number.
• Significance Level (α): Choose your desired significance level from the provided options. This dropdown has three choices: 0.01 (1%), 0.05 (5%), and 0.1 (10%). It is a required field and will impact the critical value calculation.

Step 3: Review the Calculated Results

• t-Statistic: The calculator computes the t-statistic using the formula: (Sample Mean – Population Mean) / (Sample Standard Deviation / sqrt(Sample Size)). This result is crucial for determining how extreme your sample mean is in relation to the population mean.
• Degrees of Freedom: This value is calculated as the sample size minus one (n – 1). It indicates the number of independent values in a dataset that are free to vary.
• p-Value (Two-Tailed): The p-value is calculated based on the t-statistic and the degrees of freedom. It reflects the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis.
• Null Hypothesis Result: Based on the significance level and the p-value, the result will show either “Reject H₀” if the p-value is less than the significance level, or “Fail to Reject H₀” if it is not. This is your statistical conclusion.
• Critical Value (Two-Tailed): The calculator provides the critical value at the chosen significance level using a two-tailed test. It is used as a threshold against which the t-statistic is compared.

Step 4: Interpret the Results

Assign meaning to the calculated results. If the null hypothesis is rejected, it indicates that the sample provides enough evidence to conclude that the population mean differs from the hypothesized mean. If the null hypothesis is not rejected, there is insufficient evidence to support a difference.