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
9.7	8.7
10.1	9.7
8.5	10.8
10.4	10.9
10.7	10.6
11.8	10.1
9.8	12.3
10.6	8.8
10.4	10.4
10.2	10.9
11.3	10.4
9.2	11.6
10.7	10.9
10.8
8.2

After 9 Days

Treatment	Control
138.3	9.4
104	8.8
96.4	8.8
89	10.1
88	9.7
103.8	8.7
147.3	10.3
97.1	12.3
172.6	9.4
146.3	9.5
99	8.3
122.3	8.9
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 μ_d = μ_initial − μ_9-day.)

Find the test statistic. (Round your answer to two decimal places.)

t =

Find the df.

df =

Find the P-value. (Use technology to calculate the P-value. Round your answer to three decimal places.)

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 μ_d = μ_initial − μ_9-day.)

Find the test statistic. (Round your answer to two decimal places.)

t =

Find the df.

df =

Find the P-value. (Use technology to calculate the P-value. Round your answer to three decimal places.)

P-value =

Answer 1

Ans. I will be using R to Compute the test Statistics and other values for the given question.

For part a , we are performing a paired t t-test since we are comparing the same sample after 9 days.

Our Jypothesis will be :

H0 = There is no significant difference in mean selenium levels after 9days of Treatment i.e. (ud=0)

H1=  mean selenium levels are greater after 9days of Treatment i.e. (ud <0 )

  From the above Output we can see that our t= -17.339 , df=15 and P-value=1.235e-11.

Since our P-value is less that 0.05 , We have sufficient evidence to reject H0 at 5% level of significance.

this implies that the selenium levles are greater after 9 days of treatment.

Similarly For Part b

Our hypothesis will be

H0 = There is no significant difference in mean selenium levels after 9days in the control group i.e. (ud=0)

H1= There is significant difference in mean selenium levels after 9days in the control group i.e. (ud not = 0)

From the Output , We can see that our T = 2.3863 , Df= 13 and P-value = 0.03292

Since oue P-value is < 0.05 , we have sufficient evidence to reject Our null hypothesis H0 at 5% lvl of significance.

This implies that there is significant difference in selenium levels in the control group as well at 5 % level of significance.