Statistical Tests: Z-Tests

Z-Tests are statistical tests that are used to compare population means to a sample’s. But how to interpret & calculate them?

In my other examples, I talked about an experiment to check if a medicine had a significant effect on increasing kids’ heights. We set a significance level of 0.05 and now we want to calculate the P-Value.

Here we’ll use Z Test. The Z-score tells you how far, in standard deviations, a data point is from the mean or average of a data set.

Consider original population had a mean height of 120 cm. We take a sample from the group of kids who were given medicines and the mean comes as 135 cm. Now is this far enough from the population mean that we reject the null?

First we calculate the Z-Score using the 2 means, Standard Deviation and sample size. Say the Z score comes out to be 1.5. To get its corresponding P-value, we need to check the Z table.

We need to find where the row for 1.5 intersects with the column for 0.00, which is 0.9332. However, the Z-table gives you only “less than” probabilities. So to find the probabilities more than this, we need to subtract 0.9332 from 1 which gives us 0.0668, which is > 0.05.

Therefore, we fail to reject the null hypothesis. We can never accept it :wink:

#statistics #datascience #machinelearning