An analyst is caomparing data collected from randomly assigned test subjects who
ID: 3128246 • Letter: A
Question
An analyst is caomparing data collected from randomly assigned test subjects who used two different types of hand cream (designated I and II), each for a period of six months. The subjects used one type of cream on one hand and the second on the other and reported a "softness" factor on a scale of 1 to 10 for each hand. What steps should the analyst take to determine which cream is more effective?
A. Calculate the mean difference between the right-hand results and the lefthand results, then carry out a one sample z-test.
B. Calculate the difference in means between the right-hand results and the left-hand results, then carry out a two sample z-test.
C. Calculate the mean difference between the right-hand results and the left-hand results, then carry out a one sample t-test.
D. Calculate the difference in means between the right-hand results and the left-hand results, then carry out a two sample t-test.
E. Calculate the individual differences between the Type I and Type II results for each subject, then carry out a one sample t-test for the mean difference.
Explanation / Answer
As the data is collected for the left and right hands from the same individual, so this would give us a paired data which will not be independent sample data. So, the possibility of using a two independent sample t-test or Z-test does not exist.
So, we would use a paired sample t-test in order to test the significance of the difference between the effectiveness of creams.
A paired sample t-test is done similar to a one sample t-test with only difference that the statistics we are trying to test in this case is not the population mean, but it is the mean of the difference between the scale rating of the two creams for individual observations.
So, Option E is correct.