In 1000 samples, assuming that the null hypothesis is true, how many times would you expect to commit Type I error if alpha=.05?
a. 95 times
b. 10 times
c. 50 times
d. Not enough information given to provide an answer
To answer this question, we need to understand what "committing Type I error" means and how it is related to the alpha level.
In statistical hypothesis testing, Type I error refers to rejecting the null hypothesis when it is actually true. The alpha level, represented by the symbol α, is the significance level or the probability of committing a Type I error.
In this case, the problem provides that the alpha level is 0.05, which means we are willing to accept a 5% chance of committing a Type I error. In other words, if the null hypothesis is true, we expect to reject it incorrectly in 5% of cases.
Given that we have 1000 samples, if the null hypothesis is true, we would expect to commit a Type I error in approximately 5% of the time, or 0.05 * 1000 = 50 times.
Thus, the correct answer is c. 50 times.