More intuitively, p-value answers the questions: In general, you are strongly advised to report the p-value of your tests!įormally, the p-value is the smallest level of significance at which the null hypothesis could be rejected. However, with help of modern computers, we can do it fairly easily, and with decent precision. Two approaches can be used in order to arrive at that decision: the p-value approach, and critical value approach - and we cover both of them! Which one should you use? In the past, the critical value approach was more popular because it was difficult to calculate p-value from Z-test. In sections below, we will explain to you how to use the value of the test statistic, z, to make a decision, whether or not you should reject the null hypothesis. However, if the sample is sufficiently large, then the central limit theorem guarantees that Z is approximately N(0,1).

If our data does not follow a normal distribution, or if the population standard deviation is unknown (and thus in the formula for Z we substitute the population standard deviation σ with sample standard deviation), then the test statistics Z is not necessarily normal. As Z is the standardization ( z-score) of S n/n, we can conclude that the test statistic Z follows the standard normal distribution N(0,1), provided that H₀ is true. + x n follows the normal distribution, with mean n * μ 0 and variance n² * σ. In what follows, the uppercase Z stands for the test statistic (treated as a random variable), while the lowercase z will denote an actual value of Z, computed for a given sample drawn from N(μ,σ²).

X̄ is the sample mean, i.e., x̄ = (x 1 +. , x n be an independent sample following the normal distribution N(μ, σ²), i.e., with a mean equal to μ, and variance equal to σ².

Null hypothesis test calculator