Diabetes tends to be more prevalent in urban populations, but why this is so is not fully understood. A recent study1 on mice was designed to investigate the link between diabetes and air pollution. The study involved 28 mice, with 14 randomly selected to have filtered air pumped into their cage while the other 14 breathed particulate matter that simulated common air pollution. The response variable is the amount of insulin resistance each mouse had after 24 weeks. Higher insulin resistance indicates a greater risk for developing diabetes.
1Data recreated from information in Sun et. al. (2009), "Ambient Air Pollution Exaggerates Adipose Inflammation and Insulin Resistance in a Mouse Model of Diet-Induced Obesity", Journal of the American Heart Association, 119 (4), 538-546.
(a) Is this an observational study or randomized experiment?
Randomized experiment
Observational study
(b) If we are interested in whether there is a difference in mean insulin resistance between the two groups, what are the null and alternative hypotheses?
Let the filtered air group be group 1 , and the polluted air group be group 2 .
(c) The difference in sample means from the original sample is Upper D equals x Overscript bar EndScripts Subscript 1 Baseline minus x Overscript bar EndScripts Subscript 2 Baseline equals 1.8 minus 6.2 equals negative 4.4 . The figure below shows 1000 random assignments of insulin resistant scores from the original sample to each of the two groups. Is it likely we will reject the null hypothesis?
Yes
No
(d) Using the information given in part (c), what is the p -value? Round your answer to one decimal place.
p -value equals
exact number, no tolerance
(e) State the conclusion of the test in context.
There is strong evidence that air pollution does affect insulin resistance.
There is strong evidence that air pollution has no effect on insulin resistance.
There is mild evidence that air pollution does affect insulin resistance.
There is mild evidence that air pollution has no effect on insulin resistance.
Reject Upper H Subscript 0 .
Do not reject Upper H Subscript 0 .