Question

2. When we carry out a 1-sample hypothesis test for the mean, one of the ways that we can check for normality is to look at the normal plot. How do we know if our normality assumption is satisfied by looking at the normal plot?

Answer 1

In the normal quantile-quantile plot if the actual quantiles of the data fall on the theoretical quantiles i.e. or if the deviation between the actual and theoretical quantiles is very less we can say that the data follows normal distribution. If the actual quantiles deviate from the theoretical ones, then we say that the data is non-normal. We can also perform hypothesis testing for the same. If the null hypothesis is that the theoretical quantiles and actual quantiles come from the same distribution and we fail to reject the null hypothesis, then we conclude that the data is normally distributed.