A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of the paper “Effects of Short-Term Supplementation with Selenised Yeast on Milk Production and Composition of Lactating Cows” (Australian Journal of Dairy Technology, [2004]: 199– 203) supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement (the treatment group)
and a control sample given no supplement, both initially and after a 9-day period.
Initial Measurement After 9 Days Treatment Control Treatment Control 11.4 9.1 138.3 9.3 9.6 8.7 104.0 8.8 121.5 8.2 93.0

a. Use the given data for the treatment group to determine if there is sufficient evidence to conclude that the mean selenium concentration is greater after 9 days of the selenium supplement.

b. Are the data for the cows in the control group (no selenium supplement) consistent with the hypothesis of no significant change in mean selenium concentration over the 9-day period?

c. Would you use the paired t test to determine if there was a significant difference in the initial mean selenium concentration for the control group and the treatment group? Explain why or why not.