Diabetes tends to be more prevalent in urban populations, but why this is so is not fully understood. A recent study 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.

(a) Is this an observational study or randomized experiment?

(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?

(c) The difference in sample means from the original sample is D = xÌ…_FA ˆ’ xÌ…_PM = 1.8 ˆ’ 6.2 = ˆ’4.4. Figure 4.27 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?  

Figure 4.27

(d) What is the p-value?
(e) State the conclusion of the test in context.

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