However, with help of modern computers, we can do it fairly easily, and with decent precision.
![p value form z score p value form z score](http://www.z-table.com/uploads/2/1/7/9/21795380/7807141_orig.png)
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.
#P VALUE FORM Z SCORE HOW TO#
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.
![p value form z score p value form z score](https://cdn.numerade.com/ask_images/4ea0d5b7e6af4de294039dc7fa03b668.jpg)
![p value form z score p value form z score](https://www.investopedia.com/thmb/cTLmW4BN4TGe8UizdDPTi1ld-i8=/1431x1073/smart/filters:no_upscale()/Z-dc7881981d5b4ab5a8765f2a293c9552.png)
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.