# Hypothesis Question

A bottler of iced tea wishes to ensure that an average of 16 ounces of tea is in each bottle. In order to analyze the accuracy of the bottling process, a random sample of 150 bottles is taken. Using a t-distributed test statistic of -1.09 and a 5% level of significance, the bottler should: A) not reject the null hypothesis and conclude that bottles contain an average 16 ounces of tea. B) not reject the null hypothesis and conclude that bottles do not contain an average of 16 ounces of tea. C) reject the null hypothesis and conclude that bottles contain an average 16 ounces of tea.

A

t stat = -1.09 lies in the range of the critical value i got…ie frm -1.960 - +1.960 hence we fail to reject the null and conclude that bottles do not contain an ovg of 16 ounces of tea! i hope i am correct…please post ur answers people!

what is the null and alternate hypothesis in his case. Since he wishes that average is 16, I thought Ho , u != 16 Ha, u =16 Am I incorrect?

No. If he wants to ensure that the bottles hold 16 ounces, his null is that they hold 16 ounces. He is looking for evidence to refute that claim. He fails to find the evidence based on the t-stat, and thus is not able to reject his hypothesis.

hmm…but isnt the null hypothesis supposed to be the one which he wants to reject. He wants to reject that bottles donot hold 16 ounces and thus his null shuld be mean is not equal to 16. What you are saying is correct as per the solution but am not able to undestand as per the logic am using. Please help. I have read quant but this is totally throwing off my concept of hypothesis.

I have always thought of the null as being closest to the “way we think things are.” In other words: in order to say that things AREN’T the way we think they are - or the way we expect them to be - we need a significant amount of supporting data. This would make H0, x = 16

acer Wrote: ------------------------------------------------------- > hmm…but isnt the null hypothesis supposed to be > the one which he wants to reject. He wants to > reject that bottles donot hold 16 ounces and thus > his null shuld be mean is not equal to 16. > > What you are saying is correct as per the solution > but am not able to undestand as per the logic am > using. Please help. > > I have read quant but this is totally throwing off > my concept of hypothesis. First, a null hypothesis will never be Ho != c. We always set up the null so as to hypothesize that the unknown parameter value is equal to something (or in the case of one tailed test, less than or greater than). The idea is that IF our sample creates a value for the parameter that is significantly different than our proposed value, then we can say that it is highly unlikely that our proposed value is actually legit. For example…consider the highly overused, but helpful nonetheless, bell curve. We know that for a r.v. whose mean is zero, and std. dev. is one, then there is a very small chance that a random draw will provide a value of 5.5…a value way out in the right tail. Conversely, if we ASSUME the true value is zero, and realize a value of 3.5 on a sample, we know that we have either seen a one-in-a-million event, or our assumption is incorrect about the true value of zero. Therefore, we have considerable evidence to refute the claim of mean = 0. In this example, we start with the hypothesis that the true value is equal to something (16 ounces), and look for information within a random sample that might provide evidence that the hypothesis is incorrect. If our sample mean is not far from 16, it is not unreasonable to suspect that 16 is correct.