Question

Suppose 600 different researchers each did a study to see if there was a relationship between daily coffee consumption and height for adults. Suppose there really is no such relationship in the population. Would you expect any of the researchers to find a statistically significant relationship? If so, approximately how many (using the usual criterion for "small chance" of 5%)? Explain your answer.

Answer 1

Type I error is rejecting a true null hypothesis. Before starting an experiment we generally fixed signifance level , =0.05. It means the probablity of committing type I error is 0.05 or 5 % i.e. even though null hypothesis is true there is still 5 % chance of rejecting it.

In our situation there is no relationship between daily consumption and height for adults. Based on out tests we should fail to reject null hypothesis. But due to sampling fluctuation, if the data falls in critical region, generally 5 % cases of total, then in all 5 % cases researchers to find a statistically significant relationship.

Here total number of researchers are 600. So approximately 600*0.05=30 researchers will find a statistically significant relationship.