Discussion
In statistical hypothesis of equality of means such as H0 : μ = 10, if α = 5% :
Answer: C
With α = 5%, 5% of the time we will say that there is a real difference when there is no difference.
α is the probability of a Type I error: rejecting H0 when it is true. Here H0 says the mean is 10, so rejecting it amounts to declaring a real difference from 10. If H0 is in fact true and the test is repeated many times, it will wrongly declare a difference in about 5% of cases.
Saying there is no real difference when there is none is the correct decision, which happens 95% of the time, not 5%. An incorrect inference 95% of the time reverses the figures, and α says nothing about how often the null hypothesis is true, which rules out the last option.
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