For a given inference question, follow the following thought process: a) check if it is a mean or proportions question, b) check if it is a one sample or a two sample setup , c) check conditions, and d) pick appropriate formulae.

You also need to show your work (formula setup, calculations, etc.) and state any properties or rules you need to solve the problems. Be sure to show all 4 steps of hypothesis testing and please be sure to check conditions wherever needed.

1) A product developer is interested in reducing the drying time of a primer paint. Two formulations of the paint are tested; formulation 1 is the standard chemistry, and formulation 2 has a new drying ingredient that should reduce the drying time. From experience, it is known that the drying time for formulations 1 and 2 are normally distributed with standard deviations of 8 and 9 minutes, respectively. Ten specimens are randomly selected and painted with formulation 1, and another 10 specimens are painted with formulation 2. The two sample average drying times are 121 minutes and 112 minutes for formulations 1 and 2, respectively.

(1a) Calculate and interpret a 95% confidence interval for the true average difference in drying times with the two formulations (1 2). Note: Do not do the 4 steps for part 1a). It only asks for a confidence interval and no hypothesis testing.

(1b) Can the interval above be used to test if the new formulation helps in reducing the drying time? Answer it by framing the hypotheses for this test (Step 1).