[SOUND] Now let's start on how to do the hypothesis test when we do one-tail test. Going back to the student debt and the Good Deal University's example. It is believed that the average for debt for the class of 2015 graduates is $35,000. University of Good Deal believes that their students have a lower debt amount. They survey 150 other graduates, seniors, and find the average debt to be 33,800 with a standard deviation of 10,000. At 5% level of significance, is there enough evidence to support Good Deal University's claim? We will follow the steps for performing the hypothesis testing of stating the hypothesis. Since Good Deal thinks that their students have lower than national average debt, that is the alternate hypothesis here. They need to reject the current belief that the graduates are no different than any other graduates. Specified at the significance level of 0.05. And now we will calculate the p-value based on sample information. P-value is the probability of finding a sample like we found. To answer this question, we have to calculate its t-value. So in this example, we put 33,800, the sample mean, and subtract this from the hypothesis mean of 35,000, and then the difference is divided by the sample standard deviation of 10,000, divided by the square root of the sample size of 150. The t-value for this example is negative 1.47, which means the sample we have falls 1.47 standard deviations away from the center of the distribution on the left side. The p-value is found by using the Excel function shown here. This function, again, has three arguments. The first one is the t-value, which you calculated to be negative 1.47. Second argument is the sample size minus one, which is 149. And the last argument is one. And we get the p-value of 0.0718, or roughly about 0.072. I like pictures, so let me show you what this means in pictures. Since this is a one-tail test, the entire p-value is on the left side of the mean. But the p-value is not less than 0.05. Which means, we don't have a sample that shows enough difference from the national average. So p-value is more than the alpha value. So we will not reject the null hypothesis. This means Good Deal University has failed to provide enough evidence to show that their graduates are any better off than the rest of the college graduates in the nation. This was the other example we looked at in lesson one. Now let's try to solve it together. State the hypothesis, and the level of significance. What is your hypothesis? It should look like this. Remember, the current belief is that the average ACT is greater than 24, not 24 or more. That means the correct representation is, mu is greater than 24. And since equal sign needs to be in the null hypothesis, we will put this as the alternate. And the null, becomes mu is less than or equal to 24. The specified level of significance is 0.05. And now, given the following sample information, let's start solving for the p-value. Given the sample statistics, what is the t-value? Putting the value in the equation, we get the t-value of 1.85. So what is now the p-value? If we use the same function, T.DIST, we get the value of 0.967. That is the area to the left of 1.85. >> This is the area to the left of the t-value. P-value is the area in the tail. And we have to subtract it from 1, which gives us 0.033. So what is your conclusion? Since p is less than alpha, we will reject the null hypothesis in favor of the alternate. Which means it seems the University's correct in thinking the average ACT score of the freshmen is higher than 24. When you are testing the mean, then you have three possible sets of hypotheses. If it is a test of equality versus not equal, you have two rejection regions. You will reject if your sample statistic deviates by too much from the mean in either direction. How much is too much, of course, depends on your level of significance. In case of two-tail, find the p-value, multiply it by 2, if that is less than alpha, reject the now hypothesis. If you're testing greater than or equal versus less than, or less than or equal versus greater than, then you're conducting a one-tail test. The rejection region is only on the tail that corresponds to the sign of alternate hypothesis. In case of one-tail test, reject the null hypothesis if p is less than alpha. [SOUND]