For the BRFSS example discussed in Section 13.6, there are a number of inference-making procedures that may be conducted about the joint effects of the two exposure variables exercise and tobacco_now. Using the output in Section 13.6 and below for the analyses of 1,048 individuals, do the following:
a. Test the null hypothesis H0: "The population mean BMI for an individual who exercises and doesn't use tobacco equals that for an individual who neither exercises nor uses tobacco" against the alternative that this null hypothesis is false.
b. Assess whether there is statistical evidence that the population mean BMI for an individual who exercises and uses tobacco equals that for an individual who neither exercises nor uses tobacco.
c. Describe how you would compute a 99% confidence interval for the population adjusted mean BMI of an individual who exercises and uses tobacco.
d. In a regression model not containing the two continuous covariates drink_days and poor_sleep_days, the value of β4 for tobacco_now changes from -1.108 to -0.855. Do you think that drink_days and poor_sleep_days together are confounders of the relationship between tobacco_now and BMI?

COVARIANCE OF ESTIMATES drink days poor_sleep days exercise Variable Intercept drink days poor sleep_ days exercise tobacco now Intercept 0.2280218243 0.004271369 -0.004271369 0.0006654907 tobacco now 0.003156079-0.166485871 0.055383413 0.0000211512-0.000172153 0.0006952607 0.0003314055 0.0002936177 0.000743809 0.0002936177 0.201860869 0.023262661 -0.000743809 0.023262661 0.003158079 0.0011512 0.166485871 0000172153 0.055383413 0.0006952607 0.242110744