For this question, we're looking to see if the lap time for a runner it's different in the racing context than in the practice context and were asked to use the data for Lap five from a seven lap run given in the appendix of the textbook. And I've summarises data for races and practices in terms of the sample size, the average sample time for the lap and the sample standard deviation. And I actually did this in Excel. So I copied the data for lap five out of the text book and put it here and then to calculate the mean I used this formula, the average formula and to calculate thesis sample standard deviation. I used this formula here, so let's state our hypotheses. So the no hypothesis is that there is no difference in the average lap time for races and for practices. In other words, the difference is equal to zero, and the alternative hypothesis is that there is some difference. And as we can see based on this not equal to operator, this is going to be a two tailed test, and let's decide up front that we're going to do this test at the Alfa equals 0.5 significance level, and the next step is to calculator test statistic. And because we don't have the standard e standard deviation of the population off lap times, we're relying on the sample standard deviations. And so our test statistic is distributed according to the student's T distribution, which looks like this and so we can put the valleys from the table. We're from the samples into this equation and this comes out to minors 3.307 And now, to find the corresponding P Valley, we must also have the degrees of freedom and that's given by this equation and solving that using a calculator or software, you should get a vote 20 0.32 degrees of freedom, and then we can sell for the P Value and Excel. He's the function t dot the i s t dot to t. And instead of putting minus 3.307 I'm going to put plus 3.307 which is fine because this is a two tailed test, but also because this to tail distribution in Excel is looking for the right or the positive end of the test statistic. So it's looking for the positive test statistic. So 3.307 and the degrees of freedom was 20.32 and we get a P value of 0.35 and now we can compare the P value to the significance level. And the P Valley is indeed less than Alfa. So therefore, we reject the no hypothesis and we can conclude that at the 5% significance level, there is sufficient evidence to suggest a difference in the meantime for laps in the race sitting and in the practice setting.