Question

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 averagedstudent submitted image,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 two-tailed with a=.01

Answer 1

The question does not provide enough information for a complete answer because a mean difference is necessary for calculating the t-statistic in a related samples t-test. The given median difference is not sufficient for this statistical test, and without the mean or a direct p-value, we cannot conclude whether there is a significant change in cholesterol levels as a result of adding oatmeal to the diet.

Step-by-step explanation:

To determine whether there is a significant change in cholesterol level after adding oatmeal to the diet, we use the sample data with a two-tailed test at the 0.01 alpha level.

The formula for the t-statistic in a related samples t-test is:

t = (M - μ) / (s / √n)

where M is the sample mean difference, μ is the population mean difference we are testing (often 0 for testing the null hypothesis of no change), s is the standard deviation of the difference scores, and n is the number of observations.

First, we calculate the standard deviation (s) using the sum of squares (SS) provided:

• s = √(SS / (n - 1))

Then we calculate the t-statistic using the sample mean difference (Md), assuming the null hypothesis is that the population mean difference is 0:

• t = Md / (s / √n)

In this case, since no mean difference is provided and only the median (Md) is given, we cannot compute the t-statistic without the mean. However, if we had the mean, we could calculate the t-statistic and compare it to the critical t-value at the 0.01 level for a two-tailed test with n - 1 degrees of freedom. If the calculated t is larger than the critical t, we reject the null hypothesis, indicating a significant change in cholesterol levels.

As it stands, the median difference alone is insufficient to conclude, as we would need the mean difference for a t-test or directly the p-value associated with the test to make a decision.