3. A researcher for a cereal company wanted to demonstrate the health benefits of eating oatmeal. A sample of 9 volunteers was obtained and each participant ate a fixed diet without any oatmeal for 30 days. At the end of the 30-day period, cholesterol was measured for each individual. Then the participants began a second 30-day period in which they repeated exactly the same diet except that they added 2 cups of oatmeal each day. After the second 30-day period, cholesterol levels were measured again and the researcher recorded the difference between the two scores for each participant. For this sample, cholesterol scores averaged MD = 16 points lower with the oatmeal diet with SS = 538 for the difference scores. a. Are the data sufficient to indicate a significant change in cholesterol level? Use a two-tailed test with alpha = .01. b. Write a sentence describing the outcome of the hypothesis test as it would appear in a research report.

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Video Transcript

Hi in this problem we do one sample T test for a difference of meat for me. The difference the reason why is the samples on our independence. We have we only have one set of participants and we do two trials on the So I assume on conditions for influence on that, we will start by finding the T. School. We used the T test because we only know what the sample standard deviation is. We don't know the true population standard deviation. So T will be equal to mhm. The sample mean minus the population mean over the standard error. They were called to -16 0 over 95.58 or square root of nine. That's the result in -8.92. So we grab that for a normal distribution. And look let's say thi distribution. Sorry? Okay. Um 9.82 Year round. Okay. I want to find the area to the left that point. The degree of freedom for this T distribution would be eight. The feeling is always equal to N -1. So we found a P value using the T C. D. A function on ta for graphing calculator. Or you can use a table. Um Lower band will be negative infinity. Our program will be negative April 92. Degree of freedom will be that's the result of a p value of 9.87. Eight Times 10 to the power of -6 Albums. What are we going to test the alpha level of? 0.01. So this is equal to nine It'll be 10 over 100,000. So one over 10,000 roughly. So it would be way less than 0.01. So P value is less than alpha. Yes. So we reached out into my prosthesis. Mhm. So at so for the conclusion, you would say, at the significance level of 0.01, there is sufficient evidence to show that adding oatmeal to the diet decrease cholesterol level. I hope that helps.

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