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. Authors of a research paper 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

Treatment	Control
11.3	9.1
9.6	8.7
10.1	9.7
8.5	10.8
10.4	10.9
10.6	10.6
11.9	10.1
9.9	12.3
10.8	8.8
10.4	10.4
10.2	10.9
11.3	10.4
9.2	11.6
10.6	10.9
10.9
8.2

After 9 Days

Treatment	Control
138.3	9.4
104	8.9
96.4	8.9
89	10.1
88	9.6
103.8	8.6
147.3	10.3
97.1	12.3
172.6	9.4
146.3	9.5
99	8.3
122.3	8.7
103	12.5
117.8	9.1
121.5
93

(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. (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_d = μ_initial − μ_9-day. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df

=P-value=

(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? (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_d = μ_initial − μ_9-day. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

Answer 1