For question b. What percentage of hypothesis tests would we expect to reject H0? The answer is 10%, since that is alpha, which is defined as the probability of rejecting a true null hypothesis (and...

For question b. What percentage of hypothesis tests would we expect to reject H0? The answer is 10%, since that is alpha, which is defined as the probability of rejecting a true null hypothesis (and as above, we know the null hypothesis is true).
For question c. What if the hypothesis test concludes that we reject H0? This test does indeed give the wrong answer (since we know H0 is true), indeed this is an instance of making a type 1 error. In actual hypothesis tests, type 1 errors do indeed occur - this is due to chance, there is a chance (prob = alpha) that even when H0 is true, we will reject H0. Another way to say this: "inferential statistics is not perfect" - when we reject H0 or fail to reject H0 there is always a caveat: "There is sufficient evidence at the alpha level of significance to conclude that ..." We are never supposed to say: "WeknowH0 is true or we
know
H0 is false.
For question d. Many of you gave an answer of 90% as the probability of the event: None of the 20 tests rejects H0. This is on the right track, but doesn't follow the probability rules we learned in Chapter 4. I will give you a similar example:
If I roll one 6-sided die, the probability of not getting a 1 is 5/6.If I roll two 6-sided dice, the probability of not getting (1,1) is 35/36, BUT the probability of not getting any 1's is different - it is (5/6)(5/6) = 25/26.If I roll twenty 6-sided dice, the probability of not getting any 1's is (5/6)^20 = .0261, pretty small, but not zero. So this would likely happen about 3 times out of 100 rolls of twenty dice.
For answer d. P(none of 20 hypothesis tests rejects H0) = (.90)^20 = .1216, or about 12%. So itislikely that some of your projects will have no rejections (there were 2 or 3 students where this happened). But, the probability of this happening is still about 12%.