 Hello. This is a video about one sample hypothesis testing coming up with your hypotheses. A hypothesis is a claim or statement about the property of a population. In most cases, in this course, we'll either be talking about the population proportion P or the population mean mu. There are two types of hypotheses. There is first the null hypothesis. Then there is the alternative hypothesis. Every single hypothesis test will have a null and it will have an alternative. The null hypothesis denoted by H0 or H0 is a statement that the value of a population parameter, such as a proportion or mean, which is what we'll deal with mostly in this course, is equal to some claimed value. We're going to focus on this word equal to here. So clear up a lot of confusion. The null hypothesis always includes equality. Equality can only go to the null hypothesis. The symbolic form of the null hypothesis must use one of the following symbols, less than or equal to, greater than or equal to, or just equal to. These are the only three symbols possible whenever writing out the null hypothesis. The alternative hypothesis denoted by H sub a or H sub one, or you could say H1, is the statement that the parameter has a value that is different from the null hypothesis. Equality does not go with the alternative hypothesis. The symbolic form of the alternative hypothesis must be less than, greater than, or not equal to. It can only be one of these three symbols. The signs used in the null and alternative hypothesis must be compliments of each other. For instance, this means that if you were to use less than or equal to in the null hypothesis, you would have to use greater than in the alternative. If we were to use greater than or equal to in the null hypothesis, you would have to use less than in the alternative and vice versa. And if you were to use equal to in the null hypothesis, you would have to use not equal to in the alternative hypothesis and vice versa. The wording of the question will always tell you one of these signs. It's not always going to be one specific hypothesis that it tells you the sign for is just going to tell you one of the signs for one of the hypotheses. If it contains equality, the statement has to go with a null hypothesis. If it does not contain equality, the statement has to go with the alternative hypothesis. So how about an example? A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with the standard deviation of 6.3 years. You would like to test whether the population mean time on death row could likely be 15 years. So you are testing whether the population mean on death row could likely be 15 years. Identify the hypotheses here. So every hypothesis test has a null hypothesis and an alternative hypothesis. I'm dealing with a mean, so I'm dealing with you. And the question tells us we're looking at the mean time on death row being 15 years, meaning equaling 15 years. Well, the sign equal to does that go with the null or the alternative? It has to go with the null hypothesis. Equality always goes with the null hypothesis. And what's the opposite sign of equal to? Not equal to, so that's what has to go in the alternative hypothesis. Those are the two hypotheses you need for this example. Let's do a similar example. A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with the standard deviation of 6.3 years. You would like to test whether the population mean time through dealing with a mean here on death row could likely be at least at least 15 years, at least means less than or equal to 15. So when I go to label my hypotheses, I'm talking about me since I'm dealing with less than or equal to this does include equality. So we write less than or equal to 15 as the null hypothesis. Equality always goes with the null hypothesis. What is the opposite of less than or equal to? It would have to be greater than, greater than 15 in this case. Those are the hypotheses for this example. In this example, we assume that 100 babies are born to 100 couples treated with a certain method of gender selection that is claimed to make girls more likely. We observe 58 girls and 100 babies write the hypotheses to test to claim that with the gender selection method, the proportion of girls is greater than 50% identify the hypotheses. So we're talking about proportion now we're talking P, and we're talking greater than greater than 50%, which means greater than 0.5 or 0.5. Now the null hypothesis and alternative hypothesis will be the following. She goes in front first for each of them. Since greater than does not include equality, it must be the alternative hypothesis greater than 0.5 is the alternative hypothesis. For these questions, the computer does actually want to see the 0.5 there and it doesn't want you to put a space between anything so just the heads up there. And the opposite of greater than would be less than or equal to 0.5. But oftentimes, people like to keep it simple and they will just write P equals 0.5. Either of these alternative hypotheses are perfectly acceptable. Last example, Mars Candy Company publishes that the percentage of M&Ms that are brown is 13% test to claim that the percentage of M&Ms that are brown differs from 13% identify the hypothesis. And percentages and proportions go together. So when we say 13% are really meaning 0.13. That the percentage of M&Ms that are brown differs differs so they are different. Different means not equal to. So if I write out my two hypotheses, P will go first in each of them. And since my given sign does not include equality that goes with the alternative hypothesis not equal to 0.13. The opposite of not equal to is equal to. So these are the two hypotheses for this hypothesis test. So hopefully you understand a little bit better now how to identify the hypotheses for a hypothesis test.