Okay, so here we are asked if there is a difference between this year's and last year's uh households. National Household Travel survey, if they travel more last year, before beer before that and were given that in the first year, it was 16.23 versus the second year, 17.69 with standard deviations of 4.6 and 4.42 respectively. Okay, so at first glance, it doesn't appear that they change significantly, but we will be evaluating this problem at the 5% significance level, which means that we are looking at a two tailed tests since we want to find out if they are equal or if they are not equal. So, I'm gonna do a two tailed test here. That means that we're looking at our normal distribution like this chop it off here, chop it off here. Yeah, I'd have to 5% here and the other half of the 5% there. If our statistic falls into one of these shaded regions, we will reject the null hypothesis. So what is our equation? It's going to be this blue equation right here, we'll go ahead and substitute those values of X one minus x to what we have is 16.23 minus 17.69 And the next thing we need to find out is what is S P. S. P. S are pooled. Uh Standard deviations, we can do this because our standard deviations are very close to each other and the sample sizes are large enough what our sample sizes. So I got to look up at the table. Okay, so we got 15 households and 14 households. All right, so first sample sizes 15 15 minus one is 14 and the standard deviation for that one is 4.6. So we square that and do the same thing with the other sample of 50. Okay. Of 14 minus ones. We have 13 times the standard deviation of 4.42 squared. And then we add those two. And what we get for RSP is 4.24 Great value. Okay, now we take one over each of the population or sample sizes, so that's gonna be 1/15 and won over 14. And then we and that gets us zero point negative 0.9 three. And then looking in the back of the book for our degrees of freedom, we have 27 degrees of freedom and a significance level is your point 0 to 5? Yeah, a critical value of 2.52 So obviously zero negative zero point and three is less than 2.52 And we're gonna take the absolute value since it's from both sides. Remember we're looking at that is a horrible normal graph, but are negative 0.93 lands right here and are shaded regions are right there and there. So what we do is we say that we fail to reject the null hypothesis.