H0: c = T HA: c T where: T = mean measure of interferon gamma for tea drinkers c =

H0: µ_c = µ_T

HA: µ_cT

where:

µ_T = mean measure of interferon gamma for tea drinkers

µ_c = mean measure of interferon gamma for coffee drinkers

Can the pooled two-sample t-methods be used for inference in this problem? Use both the side-by-side box-and-whisker plots AND the "standard deviation rule" to support your answer.

Eleven healthy non-tea-drinking individuals were asked to drink five or six cups of tea a day, while ten healthy non-tea and non-coffee-drinkers were asked to drink the same amount of coffee, which has caffeine but not the L-theanine that is in tea. The groups were randomly assigned. After two weeks, blood samples were exposed to an antigen and production of interferon gamma was measured. Researchers wondered if L-theanine increased the measure of interferon gamma, on average. Descriptive statistics for both types of drinks and side-by-side box-and-whisker plots are given below. Type of Drink Coffee Tea Comparison of Interferon Gamma between Tea and Coffee Drinkers 0 10 20 30 40 50 60 measure of Interferon Gamma Drink min Q1 median Q3 max mean sd n coffee 0 5.0 15.5 21.0 52 17.7 16.694 10 tea 5 15.5 47.0 53.5 58 34.818 21.085 11