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Draw conclusion based on the decision in Step 6,ie Do these data present sufficient evidence (o indicate that there is & difference in the population mean seabi...

Question

Draw conclusion based on the decision in Step 6,ie Do these data present sufficient evidence (o indicate that there is & difference in the population mean seabird densities of oiled and unoiled transects? (Answer: yes Or no)(6) Construct 9o% confidence interval for the difference between the population mean scabird densities of oiled and unoiled transects . Draw the t-curve with labels(5-5)-t4n1sk-hs(-I)ttunStep

Draw conclusion based on the decision in Step 6,ie Do these data present sufficient evidence (o indicate that there is & difference in the population mean seabird densities of oiled and unoiled transects? (Answer: yes Or no) (6) Construct 9o% confidence interval for the difference between the population mean scabird densities of oiled and unoiled transects . Draw the t-curve with labels (5-5)-t4n1 sk-hs(-I)ttun Step



Answers

Use the data and confidence level to construct a confidence interval estimate of $p,$ then address the given question. The same study cited in the preceding exercise produced these results after six months for the 198 patients given sustained care: $25.8 \%$ were no longer smoking, and these results were biochemically confirmed, but $40.9 \%$ of these patients reported that they were no longer smoking. Construct the two $95 \%$ confidence intervals. Compare the results. What do you conclude?

All right, you guys let's go and get started here. So for the surfer problem to your the first thing we need to do is we need to identify um S one squared and S two squared. So what that basically means is this um S one squared is just gonna be the larger sample variance, whereas two squared is going to be the smaller sample variance. So we have two standard deviations here, one being 7.4 8 to 96 with the other being on 7.10098 Okay, so this one obviously the top one is the bigger one, so this is gonna represent S one squared. Ok, so S one square, it's going to be this guy. Let's go ahead. And so this is going to be S one types cried squared, That's one squared squared, and then there's going to be us to square. Okay, so as one square is going to be the bigger one. So this one is just going to be Well, quite literally, that times itself and there you go, that is that that is S one squared, and this one s two squared is right there. So as to square, it's gonna be a smaller one. So this times itself. Very good. Okay, so there we go. So that is part of that is S one squared and S two square. We also need to make sure that we do right, This is square centimeters. Make sure that it's centimeters squared as well. Okay, so that's two squared in square centimeters. So for part a what we have is this thing here. Okay, so 55 point that. And then make sure we have centimeters squared when we write down our and 32 centimeters squared as well. Okay, just make sure you have the units on there because they did ask for appropriate units. Alright, so down the party identify the no alternative hypothesis. No. So the null hypothesis is gonna be uh that that row one equals row two, and in the alternative hypothesis are also called H one is they do not equal because basically the reason we know that is because the new hypotheses and that is that the heights of men and women, um the possibly the heights of men and women do not have different variances, whereas we find that uh yeah, and then the alternative is going to be they do have different variances. So that's that is our hypotheses right there. So that's part B, part C is we've got to find the value of the statistics, the statistics. All we really have to do is we have to divide the we have to divide the two variances here. And so what we do is this were to take our first variance and divide by the second variance. So I'm trying to figure out which one goes first. We want to go second. Okay, very good. Okay, that's what I thought. So our f statistic is we're going to take how statistic is, we're gonna take our first variance in this case, the bigger one and divide by the smaller one that their emphasis is great. They're very very simple process. I think they wanted us to round, if I'm not mistaken. So let me double check that. Okay, and then they want us to round four decimal places. Okay, so around four and that looks like four right there. Okay, so there it is. So that is that part of the problem there? Um and then last but at least we need to find the p value is 0.52 to five. And so with the p value is that large? Guys, we are going to have a claim that we cannot conclude that uh we cannot conclude that the heights of men and women have different variances. So because of the P value, the P value tells us. Mhm. So that we failed to conclude failed to reject. Yeah, we can say that to fail to reject the null hypothesis. And um yeah, that's pretty much it.

In this problem, we're testing for statistically significant difference in the mean waterfall. Heights between Europe and Asia were given a sample of size and nine for European waterfalls and nine Asian waterfalls as well without going through the tedium of showing you the actual calculations. The X bar for the European waterfalls is 883.2 feet. That's the X bar for the Asian waterfalls is 840 0.3. We are not given Population Sigma's, so we have to calculate those from the sample is well doing. So we get for the European waterfalls. We get a sample standard deviation okay for 3 87.2 and for the Asian waterfalls for 77.7. Now, even though the sample size is less than 30 it's reasonably safe to assume that the underlying population of waterfalls in each continent is normally distributed, and so therefore, we can take our typical approach of developing a test statistic of the form sample. Me minus my hypothesized expected value of the mean standardized by dividing by the standard error right now are no hypothesis in this circumstance is simply that the population means are equal to each other and in this case are alternative hypothesis is that they are different. That is to say, we are not making any assumption about if they're different in what direction or which one would be greater or lesser. We're simply saying they're either. Where are null hypothesis is that on average, waterfalls are justus high in Europe, as they are in Asia are alternative hypothesis is that they're not that there is a statistically significant difference between the two continents. That being the case are specific. Test statistic in this case turns into this right. The difference of the sample means minus the difference in the expected population means and divided by the standard error, which, based on sample standard deviations, looks like this. But because our no hypothesis is that these two means air equal, this term is going to translate to zero will simply go away. So therefore, our test statistic is simply going to be. The difference in the sample means over this standard error formulation. Great now, because we're not taking a position on which direction which continent would be greater or lesser. This is a to tail test, and the book specifies that we use a 10% or Alfa equals 100.10 significance level right now for the student t distribution. We need to know that the degrees of freedom of the distribution and in this case, degrees of freedom, is going to equal the lesser off the respective sample sizes each of minus one in each case. Now, in this case, both of sample sizes equal nine they're four degrees of freedom are nine minus one. In this case or eight, if I have a two tailed T distribution was an Alfa of 0.1 and eight degrees of freedom. This gives me my critical value. This could be looked up, a variety of ways to get this the critical values plus or minus one point feet +595 And therefore, if we were to visualize, this would have. So any values of the test statistic falling in this range would result in are not rejecting the null hypothesis, which is to say we would not be able to say with any statistical significance that the mean waterfall heights are different between the two continents Now, as it turns out, if we took all of those values, we had up above and plugged it into the test statistic formula. We would come up with a T statistic in this case of 0.2093 which is approximately there and clearly in the range where we do not reject are no hypothesis.


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