Tamika P.
asked • 06/14/15Probability - How to determine population parameter
Please help. A researcher collated data on American's leisure time activities She found the mean number of hours spent watching tv to be 2.7 hrs with a standard deviation of 0.2hrs. John believes football team watches less tv than 2.7 hrs; gathered 40 teammates and found the mean to be 2.3hrs. What is the correct null and alternative hypothesis?
I have Ho=mean 2.7 versus Ha mean not equal to 2.7
or
Ho not equal to 2.7 versus Ha < 2.7
I am having a hard time trying to determine when to use the population parameter of: not equal, greater than or less than.
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2 Answers By Expert Tutors
Hugh B. answered • 06/14/15
Tutor
4.9
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Experienced Mathematics/Statistics/Biostatistics Tutor
Hi,
I would respectfully disagree with the previous answer. Because John would like to be able to prove that the mean is less than 2.7 the null and alternative hypotheses that John sets up will be
Null hypothesis, HO: population mean greater than or equal to 2.7 (or you can write it as population mean = 2.7)
Alternative hypothesis, HA: population mean less than 2.7.
Here is how to think about why the alternative hypothesis is less than. Suppose I want to set up a hypothesis test that will be able to prove some point that I want to make. If I reject the null hypothesis at say a 0.05 significance level, what that means is that if the null were true, there is only a 1 in 20 chance of the null being true and generating the data I collected, so that is evidence that the null is false and the alternative is true. On the other hand, if I fail to reject the null, all I can really conclude is that this data doesn't provide evidence that the null is not true. In short, if you would like the hypothesis test to be able to provide evidence about a greater than relationship or a less than relationship, than the relationship that you want to provide evidence about has to be framed as the alternative hypothesis, because when you reject the null it is because you have evidence that the alternative is true.
Here is another example that may help to illustrate. Suppose I want to claim that a product I sell is better than some rival's product. If the alternative hypothesis is just an inequality, all the test can ever tell me is that there is no evidence of a difference between the two products (ie., if we don't reject the null) or that there is evidence of a difference between the two products, but not which product is better.
So now instead suppose we set up an alternative hypothesis that involves a directional inequality (i.e., either greater than or less than). I will pick an example product here, say light bulbs, and suppose I want to say my light bulks are better because they last longer. Then what I should do is set up the null to say that my light bulbs last the same or a lesser time and the alternative to say they last longer. Then when I run the test, if I reject the null in favor of the alternative, I can say that there is evidence that my light bulbs last longer. In contrast, suppose the null was that my light bulbs last longer, and the alternative is that my light bulbs last less time. Then if I accept the null, all I can say is that there is no evidence my light bulbs less time than the other guy's light bubs, which is clearly not as strong a claim as saying there is evidence that they last longer.
In short, note that if you want the test to be able to support a claim that you believe to be true, then you want that claim as the alternative hypothesis. Here, John believes that the mean is less than 2.7, so that should be the alternative hypothesis.
One last point to note is that writers and teachers will sometimes somewhat correctly but misleadingly say "make the alternative hypothesis the thing you want to prove." I wouldn't say it that way because when I test a hypothesis what I want to do is collect the best evidence and evaluate it in an unbiased way - what I want to learn is the truth, and I don't really want to prove anything but rather discover something. But it is the case that if I would like the hypothesis to be able to reveal that the the truth involves a directional inequality, such as that the mean is less than 2.7, then that has to be the alternative hypothesis.
Best wishes,
Hugh
Stephanie M.
tutor
Hi Hugh,
You haven't really disagreed with what I said; you've just picked one of the two options I gave the student.
The reason I gave two options is that the student gave us two possibilities and Ha: mean < 2.7 / H0: mean ≥ 2.7 is not one of them. I agree that, based on the problem, that's the best way for John to set up his hypotheses. That's why I included it despite the fact that it doesn't matching either of the given choices.
Of the two given choices, however, the only possible answer is the first one. The second option's null hypothesis isn't the complement of its alternative hypothesis, and therefore the experiment fails to consider the possibility that the football players' mean is greater than Americans' mean.
Hope this clarifies!
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06/14/15
Hugh B.
Yes, I see now that we don't disagree, except that I would allow that the null hypothesis can be written as an equality and the alternative as a directional inequality mainly because I have been forced to use texts that teach that. So really what I should have said is that you may see authors who will combine H0 as "=" with HA as "<" or ">" but I also agree with you that the null and alternative should be an event A and A complement. I think the reason that the text I was assigned combined H0 "=" with HA "<" or ">" is probably that it wanted to say that we assume the null hypothesis to be true when we conduct the test and it then wanted to just be able to plug in whatever the null said the mean was equal to, rather than go to the trouble of explaining that if the null was greater than or equal then we should use the smallest value.
I think my misunderstanding is that I did not understand this to be a multiple choice exam where they pick the best answer, but rather their answers that they were offering. The point I was trying to make is that in general hypothesis testing doesn't provide evidence about the null being true (unless there is a specific value specified as the alternative hypothesis). I think students need to understand that failing to reject the null is not the same as believing that the null is true or providing evidence that the null is true. In fact, in this hypothesis testing situation as in many, because the sampling distribution of the mean is a continuous distribution, the probability that the population mean is 2.7 is 0.
I hope I have given no offense - sure didn't mean to.
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06/14/15
Hugh B.
Hi Tamika,
I will provide one last set of comments on hypothesis testing that will hopefully provide some insight about how to set up hypothesis tests. I will include some more examples that may also be helpful.
When we test the null hypothesis against an alternative hypothesis, we assume that whatever value that the null hypothesis says is the mean is in fact the mean when we construct the test statistic. The reason we do that is that we want to see if the sample will provide evidence that the null hypothesis is false. This setup implies that there is a real asymmetry in the evidence about the null hypothesis that the sample is able to provide. If we reject the null hypothesis, then we reject it because we have evidence against it and in favor of the alternative hypothesis. That evidence against the null consists of a value of a test statistic computed from our sample that is a very unlikely value for the test statistic if the null hypothesis is true. On the other hand, if we do not reject the null hypothesis, that doesn't provide any new evidence in favor of the null hypothesis, it just means we can't rule the null hypothesis out as unlikely on the basis of the evidence provided by the sample we have.
An analogy that has been used that people sometimes find helpful is that in the US criminal court system the defendant is assumed innocent and the prosecution tries to prove them guilty. If the prosecution cannot prove the defendant is guilty that doesn't mean that they have proven the defendant to be innocent, they have just failed to prove guilt and the assumption of innocence gets to stand as the outcome. Similarly in hypothesis testing, the null hypothesis is assumed to be true in order to assess the evidence that it is false and there is either evidence against it or not, but it is not proven to be true when it isn't rejected as false. (I don't particularly like the analogy because we hear so many stories of mistaken convictions, but I mention it because some find it a helpful analogy.)
So in general, when we test a hypothesis we assume that the null hypothesis is true and if there is no evidence against the null then that assumption is not proven, but not disproven either. This means that if there is something that we would like to be able to find evidence for, it has to be set up as the alternative hypothesis because we are not really providing any evidence that the null hypothesis is true when we fail to reject it but we are providing evidence that the alternative is true when we reject the null hypothesis.
In terms of actual practice, it seems like we most often just want to test the null hypothesis of "same" (=) or "different" (≠) – for example, that two population means are equal or not equal, or that a single population mean is equal to some constant that we hypothesize or not equal to that constant. These are so-called two tailed hypothesis tests because the evidence against the null hypothesis can come from either a value of the test statistic that is so large that the null hypothesis is unlikely or because the test statistic has a value that is so small that the null hypothesis is unlikely. In other words, the unequal (≠) that is specified by the alternative hypothesis is either unequal because it is in the "too big" right tail of the probability distribution of the test statistic or the "too small" left tail of the probability distribution of the test statistic, hence the name two tailed test.
However, even though there are probably fewer instances where one tailed alternative hypotheses are used (that is, alternative hypotheses that are expressed as either ">" or "<," ) the examples where they are used tend to be examples where it is critically important to use them and set them up correctly. For example, new drugs are typically tested in clinical trials against a placebo (i.e., sugar pill that should have no effect). Suppose for instance, that in a clinical trial for a drug that claims to lower blood pressure (BP) the drug is tested against a sugar pill. How should we set up the null and alternative hypotheses? It should be clear that a null hypothesis that the two treatments drug and sugar pill lower BP by the same amount (i.e., =) and an alternative that they lower BP by a different amount (≠) isn't acceptable because we could reject the null even if the evidence was that the new drug did significantly worse at lowering BP than a sugar pill (which would in practice probably mean that a drug that would be marketed as lowering BP would in fact raise BP). So instead we have to set this up as the null hypothesis is that the placebo does at least as well the drug (average reduction in BP from placebo ≥ average reduction in BP from drug) against the alternative hypothesis that the drug reduces BP by more than the placebo (average reduction in BP for placebo < average reduction in BP from drug). Again, the reason for that is that if we are able to reject that null hypothesis then it will be because we have evidence that the drug does better than the placebo at lowering BP. If we are not able to reject that null hypothesis then there is no evidence that the drug does better than a placebo and therefore no reason to permit the manufacturer to claim that the drug has a therapeutic effect that is any greater than a sugar pill would have.
As one last similar example, suppose that there is some chemical, say Selenium, present in food that is harmless (and maybe even helpful) at low levels but starts being toxic at levels greater than K parts per million, where K is some number whose value an MD could tell you but I can't because I am not an MD. Suppose we collect say 50 samples of food from a possibly contaminated area and want to test whether it is safe because it has low levels of Selenium or toxic because of too high levels of Selenium. Hopefully it is clear that we do not want to test the null hypothesis that the population mean level of Selenium in the area = K parts per million against the alternative hypothesis that the population mean level of Selenium in the area ≠ K parts per million, because then if we reject the null hypothesis it could be because the food has either extremely low levels of Selenium (very safe) or because the food has extremely high levels of Selenium, (i.e., very toxic). Instead, we (or at least, I) would set this up with the null hypothesis being that the food has an average greater than or equal to K parts of Selenium and the alternative being that the food has an average less than K parts per million because then if we conclude that there is evidence against the null hypothesis it means that the food is safe. If we do not reject the null hypothesis in this example, that means that we do not conclude that the food is toxic, only that we don't have evidence that it is safe (so please don't eat it). If we had set the null hypothesis as that the food has less than or equal to K parts per million (again, recall that is an assumption that we are going to test) and the alternative that it has more than K parts per million and is unsafe, then we would have evidence that the food is unsafe if we reject the null hypothesis and would be able to say that there is no evidence that the food is unsafe if we do not reject the null hypothesis. Personally, I would rather have evidence that the food I eat is safe rather than no evidence that it is toxic so I would use the null hypothesis that says that the food has K or more parts per million of Selenium on average, but I suppose that people can disagree on that. But it should be clear that the two tailed test is not helpful here.
Lastly two rules of thumb about constructing null and alternative hypotheses:
1) We are going to use the null hypothesis to provide a value for the mean that we use when we compute the test statistic, so the null hypothesis needs to include equal as a possibility. It may be that the null is =, it may be that the null is ≥, or it may be that the null is ≤, but it should include equal as a possibility.
2) As my Wyzant colleague Stephanie says, the alternative hypothesis should be whatever is possibly true when the null is false. (You can find textbook authors who will combine a null hypothesis "=" and alternative hypothesis of say "<", so that nothing seems to allow for the possibility of ">". Stephanie and I agree this is bad practice even though you may see it.)
If we take 1 and 2 together, we can see that the possibilities for null and alternative are (null =, alternative ≠) (null ≥, alternative <) and (null ≤, alternative >). Then as I said before, if you have a particular belief that you would like to be able to find evidence for, make that the alternative hypothesis.
Hope this helps. Please feel free to ask question(s) if not.
Best wishes,
Hugh
I will provide one last set of comments on hypothesis testing that will hopefully provide some insight about how to set up hypothesis tests. I will include some more examples that may also be helpful.
When we test the null hypothesis against an alternative hypothesis, we assume that whatever value that the null hypothesis says is the mean is in fact the mean when we construct the test statistic. The reason we do that is that we want to see if the sample will provide evidence that the null hypothesis is false. This setup implies that there is a real asymmetry in the evidence about the null hypothesis that the sample is able to provide. If we reject the null hypothesis, then we reject it because we have evidence against it and in favor of the alternative hypothesis. That evidence against the null consists of a value of a test statistic computed from our sample that is a very unlikely value for the test statistic if the null hypothesis is true. On the other hand, if we do not reject the null hypothesis, that doesn't provide any new evidence in favor of the null hypothesis, it just means we can't rule the null hypothesis out as unlikely on the basis of the evidence provided by the sample we have.
An analogy that has been used that people sometimes find helpful is that in the US criminal court system the defendant is assumed innocent and the prosecution tries to prove them guilty. If the prosecution cannot prove the defendant is guilty that doesn't mean that they have proven the defendant to be innocent, they have just failed to prove guilt and the assumption of innocence gets to stand as the outcome. Similarly in hypothesis testing, the null hypothesis is assumed to be true in order to assess the evidence that it is false and there is either evidence against it or not, but it is not proven to be true when it isn't rejected as false. (I don't particularly like the analogy because we hear so many stories of mistaken convictions, but I mention it because some find it a helpful analogy.)
So in general, when we test a hypothesis we assume that the null hypothesis is true and if there is no evidence against the null then that assumption is not proven, but not disproven either. This means that if there is something that we would like to be able to find evidence for, it has to be set up as the alternative hypothesis because we are not really providing any evidence that the null hypothesis is true when we fail to reject it but we are providing evidence that the alternative is true when we reject the null hypothesis.
In terms of actual practice, it seems like we most often just want to test the null hypothesis of "same" (=) or "different" (≠) – for example, that two population means are equal or not equal, or that a single population mean is equal to some constant that we hypothesize or not equal to that constant. These are so-called two tailed hypothesis tests because the evidence against the null hypothesis can come from either a value of the test statistic that is so large that the null hypothesis is unlikely or because the test statistic has a value that is so small that the null hypothesis is unlikely. In other words, the unequal (≠) that is specified by the alternative hypothesis is either unequal because it is in the "too big" right tail of the probability distribution of the test statistic or the "too small" left tail of the probability distribution of the test statistic, hence the name two tailed test.
However, even though there are probably fewer instances where one tailed alternative hypotheses are used (that is, alternative hypotheses that are expressed as either ">" or "<," ) the examples where they are used tend to be examples where it is critically important to use them and set them up correctly. For example, new drugs are typically tested in clinical trials against a placebo (i.e., sugar pill that should have no effect). Suppose for instance, that in a clinical trial for a drug that claims to lower blood pressure (BP) the drug is tested against a sugar pill. How should we set up the null and alternative hypotheses? It should be clear that a null hypothesis that the two treatments drug and sugar pill lower BP by the same amount (i.e., =) and an alternative that they lower BP by a different amount (≠) isn't acceptable because we could reject the null even if the evidence was that the new drug did significantly worse at lowering BP than a sugar pill (which would in practice probably mean that a drug that would be marketed as lowering BP would in fact raise BP). So instead we have to set this up as the null hypothesis is that the placebo does at least as well the drug (average reduction in BP from placebo ≥ average reduction in BP from drug) against the alternative hypothesis that the drug reduces BP by more than the placebo (average reduction in BP for placebo < average reduction in BP from drug). Again, the reason for that is that if we are able to reject that null hypothesis then it will be because we have evidence that the drug does better than the placebo at lowering BP. If we are not able to reject that null hypothesis then there is no evidence that the drug does better than a placebo and therefore no reason to permit the manufacturer to claim that the drug has a therapeutic effect that is any greater than a sugar pill would have.
As one last similar example, suppose that there is some chemical, say Selenium, present in food that is harmless (and maybe even helpful) at low levels but starts being toxic at levels greater than K parts per million, where K is some number whose value an MD could tell you but I can't because I am not an MD. Suppose we collect say 50 samples of food from a possibly contaminated area and want to test whether it is safe because it has low levels of Selenium or toxic because of too high levels of Selenium. Hopefully it is clear that we do not want to test the null hypothesis that the population mean level of Selenium in the area = K parts per million against the alternative hypothesis that the population mean level of Selenium in the area ≠ K parts per million, because then if we reject the null hypothesis it could be because the food has either extremely low levels of Selenium (very safe) or because the food has extremely high levels of Selenium, (i.e., very toxic). Instead, we (or at least, I) would set this up with the null hypothesis being that the food has an average greater than or equal to K parts of Selenium and the alternative being that the food has an average less than K parts per million because then if we conclude that there is evidence against the null hypothesis it means that the food is safe. If we do not reject the null hypothesis in this example, that means that we do not conclude that the food is toxic, only that we don't have evidence that it is safe (so please don't eat it). If we had set the null hypothesis as that the food has less than or equal to K parts per million (again, recall that is an assumption that we are going to test) and the alternative that it has more than K parts per million and is unsafe, then we would have evidence that the food is unsafe if we reject the null hypothesis and would be able to say that there is no evidence that the food is unsafe if we do not reject the null hypothesis. Personally, I would rather have evidence that the food I eat is safe rather than no evidence that it is toxic so I would use the null hypothesis that says that the food has K or more parts per million of Selenium on average, but I suppose that people can disagree on that. But it should be clear that the two tailed test is not helpful here.
Lastly two rules of thumb about constructing null and alternative hypotheses:
1) We are going to use the null hypothesis to provide a value for the mean that we use when we compute the test statistic, so the null hypothesis needs to include equal as a possibility. It may be that the null is =, it may be that the null is ≥, or it may be that the null is ≤, but it should include equal as a possibility.
2) As my Wyzant colleague Stephanie says, the alternative hypothesis should be whatever is possibly true when the null is false. (You can find textbook authors who will combine a null hypothesis "=" and alternative hypothesis of say "<", so that nothing seems to allow for the possibility of ">". Stephanie and I agree this is bad practice even though you may see it.)
If we take 1 and 2 together, we can see that the possibilities for null and alternative are (null =, alternative ≠) (null ≥, alternative <) and (null ≤, alternative >). Then as I said before, if you have a particular belief that you would like to be able to find evidence for, make that the alternative hypothesis.
Hope this helps. Please feel free to ask question(s) if not.
Best wishes,
Hugh
Report
06/15/15
Stephanie M.
tutor
No offense taken! Just wanted to make sure it was clear to the student that she wasn't getting two completely different answers, just two different perspectives on what amounts to the same answer. Other than that, your explanation was excellent!
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06/15/15
Stephanie M. answered • 06/14/15
Tutor
5.0
(888)
Private Tutor - English, Mathematics, and Study Skills
Your null hypothesis is always going to support the idea that the population being studied is the same as the expected mean. In this case, we expect a sub-group of Americans to match the researcher's data: mean of 2.7 hours watching TV with a standard deviation of 0.2 hours.
So, if the population of football players matches the population of normal Americans, we expect them to have a mean of 2.7.
Thus, the null hypothesis is that the mean = 2.7.
The alternative hypothesis must be the opposite of that: that the mean ≠ 2.7.
If we wind up rejecting the null hypothesis here, John will have proven that the football players likely watch a different amount of TV than regular Americans.
You could also start with the alternative hypothesis. John believes the football players watch less TV than the average group of Americans.
Thus, the alternative hypothesis is that mean < 2.7.
The null hypothesis must be the opposite of that: that the mean ≥ 2.7.
If we wind up rejecting the null hypothesis here, John will have proven that the football players likely watch less TV than regular Americans.
In any case, the null hypothesis and the alternative hypothesis together should cover all possibilities. Only your first option does that.
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Hugh B.
I will provide one last set of comments on hypothesis testing that will hopefully provide some insight about how to set up hypothesis tests. I will include some more examples that may also be helpful.
When we test the null hypothesis against an alternative hypothesis, we assume that whatever value that the null hypothesis says is the mean is in fact the mean when we construct the test statistic. The reason we do that is that we want to see if the sample will provide evidence that the null hypothesis is false. This setup implies that there is a real asymmetry in the evidence about the null hypothesis that the sample is able to provide. If we reject the null hypothesis, then we reject it because we have evidence against it. That evidence against the null consists of a value of a test statistic computed from our sample that is a very unlikely value for the test statistic if the null hypothesis is true. On the other hand, if we do not reject the null hypothesis, that doesn't provide any new evidence in favor of the null hypothesis, it just means we can't rule it out as unlikely on the basis of the evidence provided by the sample we have.
An analogy that has been used that people sometimes find helpful is that in the US criminal court system the defendant is assumed innocent and the prosecution tries to prove them guilty. If the prosecution cannot prove the defendant is guilty that doesn't mean that they have proven the defendant to be innocent. Instead, they have just failed to prove guilt and the assumption of innocence gets to stand as the outcome. Similarly in hypothesis testing, the null hypothesis is assumed to be true in order to assess the evidence that it is false and there is either evidence against it or not, but it is not proven to be true when it isn't rejected as false. (I don't particularly like the analogy because we hear so many stories of mistaken convictions, but I mention it because some find it a helpful analogy.)
So in general, when we test a hypothesis we assume that the null hypothesis is true and if there is no evidence against the null then that assumption is not proven, but not disproven either. This means that if there is something that we would like to be able to prove, it has to be set up as the alternative hypothesis because we are not really providing any evidence that the null hypothesis is true when we fail to reject it.
In terms of actual practice, it seems like we most often just want to test the null hypothesis of "same" (=) or "different" (≠) – for example, that two population means are equal or not equal, or that a single population mean is equal to some constant that we hypothesize or not equal to that constant. These are called two tailed hypothesis tests because the evidence against the null hypothesis can come from either a value of the test statistic that is so large that the null hypothesis is unlikely or because the test statistic has a value that is so small that the null hypothesis is unlikely. In other words, the unequal that is specified by the alternative hypothesis is either unequal because it is in the "too big" right tail of the probability distribution of the test statistic or the "too small" left tail of the probability distribution of the test statistic, hence the name two tailed test.
However, even though there are probably fewer instances where one tailed alternative hypotheses are used (that is, alternative hypotheses that are expressed as either ">" or "<,") the examples where they are used tend to be examples where it is critically important to use them and set them up correctly. For example, new drugs are typically tested in clinical trials against a placebo (i.e., sugar pill that should have no effect). Suppose for instance, that in a clinical trial for a drug that claims to lower blood pressure (BP) the drug is tested against a sugar pill. How should we set up the null and alternative hypotheses? It should be clear that a null hypothesis that the two treatments drug and sugar pill lower BP by the same amount (i.e., =) and an alternative that they lower BP by a different amount (≠) isn't acceptable because we could reject the null even if the new drug did worse at lowering BP than a sugar pill (which would probably mean that it raises BP, which is the opposite of the effect it will be marketed for). So instead we have to set this up as the null hypothesis is that the placebo does at least as well the drug (H0: average reduction in BP for placebo ≥ average reduction in BP by the drug) against the alternative hypothesis that the drug reduces BP by more than the placebo (HA: average reduction in BP by placebo < average reduction in BP for the drug). Again, the reason for that is that if we are able to reject that null hypothesis then it will be because we have evidence that the drug does better than the placebo at reducing BP and thus we have evidence that the drug is effective. If we are not able to reject that null hypothesis then there is no evidence that the drug does better than a placebo and therefore no reason to permit the manufacturer to claim (i.e., tell the lie) that the drug has a therapeutic effect.
As one last similar example, suppose that there is some chemical, say Selenium, present in vegetables that is harmless (and maybe even helpful) at low levels but starts being toxic at levels greater than K parts per million, where K is some number whose value an MD could tell you but I can't because I am not an MD. Suppose we collect say 50 samples of vegetables grown in a possibly contaminated area and want to test whether the food is safe because it has low levels of Selenium or toxic because of too high levels of Selenium. Hopefully it is clear that we do not want to test the null hypothesis that the average level of Selenium = K parts per million against the alternative hypothesis that the average level of Selenium is ≠ K parts per million, because then if we reject the null hypothesis it could be because the food has either extremely low levels of Selenium (i.e., very safe) or because the food has extremely high levels of Selenium, (i.e., very toxic). Instead, we (or at least, I) would set this up with the null hypothesis being that the food has an average greater than or equal to K parts of Selenium and the alternative being that the food has an average less than K parts per million because then if we conclude that there is evidence against the null hypothesis it means that the food is safe. Of course, if we do not reject the null hypothesis in this example, we do not conclude that the food is toxic, only that we don't have evidence that it is safe (so please don't eat it). If we had set the null hypothesis to be that the population mean for the food ≤ K parts per million (again, recall that is an assumption that we are going to test) and the alternative that the population mean > K parts per million and is unsafe, then if we rejected the null hypothesis we would have evidence that the food is unsafe and if we do not reject the null hypothesis we would be able to say that there is no evidence that the food is toxic. Personally, I would rather have evidence that the food I eat is safe rather than no evidence that it is toxic so I would use the null hypothesis that says that the food has K or more parts per million of Selenium on average, but I suppose that people can disagree on that. Anyway, it should be clear that the two tailed test is not helpful here.
Lastly two general rules about constructing null and alternative hypotheses:
1) We are going to use the null hypothesis to provide a value for the mean that we use when we compute the test statistic, so the null hypothesis should include equal as a possibility. It may be that the null is =, it may be that the null is ≥, or it may be that the null is ≤, but it should include equal as a possibility.
2) As my Wyzant colleague Stephanie says, the alternative hypothesis should be whatever is possibly true when the null is false. (Although you can find textbook authors who will combine a null hypothesis "=" with an alternative hypothesis of say "<", so that nothing seems to allow for the possibility of ">" my colleague Stephanie and I agree this is bad practice.)
If we take 1 and 2 together, we can see that the possibilities for null and alternative are (null =, alternative ≠, i.e., a two tailed test) (null ≥, alternative <, one tailed test with evidence against the null in the left or "test statistic too small" tail) and (null ≤, alternative >, one tailed test with evidence against the null in the right or "test statistic too large" tail). Then as I said before, if you have a particular belief that you would like to be able to find evidence for, make that the alternative hypothesis.
Best wishes for success with your class, hopefully you will come to enjoy statistics as a lifelong tool for discovery, as I do. Hope this helps in that direction, but please feel free to ask question(s) if not.
Kind regards,
Hugh
06/15/15