All right for this question they are asking us to find first the null hypothesis in the alternative hypothesis is so we have a claim that the freshman students on a campus study at least 2.5 hours per day. The null hypothesis is that claim so freshman study at least greater than equal to 2.5 hours for a day. And the alternative hypothesis is what the statistics cost. They're skeptical of this claim. So the alternative hypothesis is that freshman studied less than 2.5 hours per day. So what we need to do is we need to figure out is this null hypothesis Is this claim true? In order to do that, we need to find the p value. So in order to find the P value, the first thing we need to do is find the test statistic on that shows us how many standard deviations away from the mean is the results. So our T statistic, we find that with the formula of the, um, sample me and minus the population mean over the sample standard deviation over the square root of the sample size. So when we put that information in, Um, we're gonna go ahead and convert the minutes in the problem. Two hours. Um, to do that, you just divide by 60. So we have our 137 minutes becomes too point to a hours minus 2.5 hours over the sample standard deviation, which is, um, 0.75 hours, 45 minutes. It's 450.75 hours divided by the square root of the sample size, which is 30. And when you put that in your calculator, you get negative 1.6 07 Now that we have our t score, um, we need to find the P value. To do that, all you need to do is look up a tea table. You can even just google that and you'll find a tea table. You find negative 1.6 of seven, and it will give you the P value. The P value that you are given with that, um, to score is 0.6 now. What this means is that the probability of getting 137 minutes as the means so that's the 2.28 hours in the study is basically a 6% chance if the null hypothesis is true. So in order to decide about this study, we need to know what Alfa is. Alfa is the significance level. So Alfa is the probability of rejecting the null hypothesis when in fact it's actually true. The Alfa that they gave us is 0.1 which means that 1% of the time on the threshold is 1% of the time. You would reject the normal hypothesis when, actually it's true. Our P value, as we've already found, is 0.6 If the P value is higher than the Alfa, then that means that we do not reject the NOL. We keep the null. So go ahead and write for our d um, that we failed to rejection and all the P value. When the pea value is high, then all flies. When the people you is low, the norm must go. So that's a little saying to help you remember. So since the P value is greater than Alfa, then re failed to reject. So our conclusion in summary is that the student claim that freshman study at least two enough hours today is correct hours per day, and what it means is that we at least it's true. Um, what it means is that at least we don't have enough evidence to say that that's not true. So we're going to say that, according to this study, that the null hypothesis we cannot reject it, that it is still true that freshman students study at least 2.5 hours pretty.