10.18: It has been claimed that no more then 5% of the units coming off an assembly line are defective. Formulate a null hypothesis and an alternative hypothesis for this situation. Will the test be one-tail or two tails? Why? If the test is one tail, will it be left-tail or right tail? Why?
So would it then be written as
Null hypothesis: Ho: π = ≤ 0.05
Alternative hypothesis: H1(the one is saposed to be down at the bottom of the H but could not get it to come up on the screen) : π = > 0.05
From what I am seeing in the book the purpose of conducting the test is to determine whether the population proportion of defective units could be greater then 0.05.
If I am understanding this correctly the test would be one-tailed because the null hypothesis is directional.
The sample that is given in the book states that a supplier claims that "no more the 20% of the cans are dented" and is listed as a right-tail test.
So since this is similar in that it states that no more than 5% of the units coming off an assembly line are defective then it would also be considered "a right-tailed test". As the center of the hypothesized distribution is identified as π = 0.05 which is the highest value for which the null hypothesis could be true, it also states that the null hypothesis tends to get the benefit of the doubt. I am just wanting to make sure that I am understanding this correctly.
You are correct. The rejection region is dictated by the alternative hypothesis. It is a right tailed test because the alternative hypothesis has a >. Personally, I'm not crazy about the terminology "gets the benefit of the doubt". I like to think of it as analogous to innocent until proven guilty. They are making a claim, hopefully based on some research, and so the "burden of proof" is on you to prove that they are wrong.