Question

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. The following data on the initial milk selenium concentration (mg/L) for a sample of cows given a selenium supplement (treatment group) is given below:

Initial Measurement Treatment 11.4, 9.6, 10.1, 8.5, 10.3, 10.6, 11.8, 9.8, 10.9, 10.3, 10.2, 11.4, 9.2, 10.6, 10.8, 8.2

Carry out a complete hypothesis testing to determine if initial mean selenium concentration is different from 11 mg/L. Use significance level of α = 0.05

Answer 1

We find the mean and standard deviation of the given data as :

We conduct T-test for one population mean as :

Hence, we conclude that initial mean selenium concentration is different from 11 mg/L at 5% level of significance.