Question

Problem 1) Consider the example we used in class on daily activity and obesity. Briefly, 10 lean and 10 obese volunteers were recruited to wear a sensor that monitored their every move for 10 days. The time that each subject spent walking/standing, sitting, and lying down were recorded. For more details see example 21.2 in the text. In addition to the variable we looked at in class, the data were analyzed to see if there was a difference in the average time the subjects spent lying down. For lean subjects (group 1) the sample mean time was 502 with sample standard deviation of 52. For obese subjects (group 2) the sample mean time was 492 with sample standard deviation of 47.

a) Verify the conditions for inference using the t distribution. The distributions are shown below; the top group is obese people, and the bottom group is lean people

b) Conduct a 4-step significance test to determine if there is evidence of a difference in the average time the subjects spent lying down. Be sure to state the conclusion in the context of the problem, not statistics jargon.

c) Calculate a 95% confidence interval. (Hint: it should look very odd.) Remember that with a quantitative response variable, a 95% confidence interval leads to a two-tailed significance test with α = 0.05 as our cutoff. If we reject Ho, then we would not expect µ0 to be inside the confidence interval. Look at your confidence interval. Does it contain the value for µ0? Look at the conclusion of the significance test. Are they consistent?

Answer 1