Question

You are currently examining the impact that meditation has on the ability to mentally focus. You have taught 100 people to meditate and on a test to measure ability to focus they scored an average of 68.3 (St Dev = 8.4). You have access to a very large experiment done between the years of 1990 and 2015 that determined that the average person scores 72.5 (St Dev = 12) on the same test (higher scores mean you can focus better). What would you conclude?     

Answer 1

Here we can test if the 100 people we taught have a lesser ability to focus. To test the hypothesis we can perform one sample Z-test for the mean.

The test statistic is given by:

The test statistic follows a standard normal distribution under the null hypothesis. Thus the p-value is P(Z<-3.5) =  0.00023.

Hence we can conclude at the level of significance of 0.01, that the testing ability of the people we taught have lesser ability to focus than the previous experiment.