Thread: Could someone check to see if I answered this correctly(2):

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.
Thanks!

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.

Correct

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.
Thanks!

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.

By the way, it would be better if your post's subject described the problem rather than what you have. For one thing, you have two posts with the same title and without going into them, I could not tell which is which. Thanks!

Thanks for the tip on the title post and also the response to my post. I think for the next time I will post the question number as the descriptive title if I have more than one post in the future.