Question

6. Consider the experiment in Exercise 3. Suppose some of the chickens were lost during the course of the experiment, resulting in the following set of observations.

Treatment	Serum T3, (ng/dl) x 10(-1)
Premolt	90.09	90.45	99.38	73.56
Fasting	98.81	103.55	115.23	129.06	117.61
60g bran	197.18	207.31	177.5
80 g bran	102.93	117.51	119.92	112.01	101.1
Laying mash	82.94	83.14	89.59	87.76

1. Write the linear statistical model for this study, and explain the model components.
2. State the assumptions necessary for an analysis of variance of the data.
3. Compute the analysis of variance for the data.
4. Compute the least squares means and their standard errors for each treatment.
5. How has the loss of some chickens from the experiment affected the estimates of the means?
6. Compute the 95 % confidence interval estimates of the treatment means.
7. Test the hypothesis of no differences among means of the five treatments with the F test at the .05 level of significance.
8. Write the normal equations for the data.

Answer 1

The linear model is given as

Yi = ₀ + _i       i=1,2,3,4,5.

Where Y i is yield from ith treatment

             ₀    General mean effect

            _i         Effect due to ith treat treatment   

Assumptions

Data is and errors normally distributed.

All variances are equal.

No correlation between erros

Hypotheisis test

Ho: All treatment means are equal

H1:At least one treatment mean is different.

SST=25054.8972         Sum of squares due treatments

MSST=6263.7243           Mean sum of squares due to treatments.

SSE=1701.13814 Sum of squares due errors

MSSE=106.321134             Mean sum of squares due to errors.

F=MST/MSE=58.9132

P=0.00000000226

Since p value < 0.05 we reject H0

Concluded that there is a significant difference between the treatments.That at least one treatment mean is different.