Please, help, this is so confusing!
For the Email Spying Example, you have said that when we wanted to test if email
open rate was higher than 40%, the null hypothesis actually had to state the
opposite. In that case:
Null Hypothesis: Population Mean open rate <= 40
Alternative Hypothesis: Population Mean open rate > 40
However in the exercise you said “What if the question was: is the
competitor open rate EXACTLY 40%?” and then the null hypothesis doesn’t state the opposite. Why is that?
I think this is because null hypothesis always includes equal to sign and hence population open rate is exactly 40% becomes the Null hypothesis.
I would request faculty to answer this as I have the same doubt.
Personally, I also got stuck on this exercise question “What if the question was: is the competitor open rate EXACTLY 40%?”
From my knowledge when you set a Null Hypothesis, it got to be a fact. So for the Email Spying example, " Your company has a 40% open rate" this is a fact and you would like to find out (or challenge) your competitor "open rate >40%?".
Ho open rate <= 40%
H1 open rate > 40%
Let's go back to this question, “What if the question was: is the competitor open rate EXACTLY 40%?”. From this statement, I could reword it to "is the competitor open rate more than or less than 40%?". so the word EXACTLY is the alternative hypothesis. That is why the below hypothesis is valid
Null hypothesis: open rate is 40%
Alternative hypothesis: open rate is NOT 40%