7. seminar
Problem 1
Eleven equally-old piglets were drawn randomly from a population of a particular race. Six
of them had been served superalimentation I and remaining five superalimentation II for
a half year. The mean daily increases in weight were recorded (in Dg.):
superalimentation I: 62, 54, 55, 60, 53, 58
superalimentation II: 52, 56, 49, 50, 51.
The data are assumed to be realization of two independent random samples following
distributions N(1, 2
1) and N(2, 2
2).
a) Determine the 95% confidence interval estimate for a quotient of population variances
2
1
2
2
.
b) Assuming that the data follow distributions N(1, 2
) and N(2, 2
), determine the
95% confidence interval estimate for the difference of the expected values 1 - 2.
To make the calculation easier realizations of following sample statistics are available:
m1 = 57 m2 = 51, 6 s2
1 = 12, 8 s2
2 = 7, 3
Problem 2
Using the data from exercise 1 test at  = 0.05 the hypothesis that:
a) the variances of increases in weight are equal (irrespective of the type of superali-
mentation).
b) both superalimentation have the same effect on the piglets' increases in weight.
Use both confidence interval method and classical method of hypothesis testing.
Problem 3
a) Six farrows and in each farrow two siblings were drawn randomly. One of them had
been served superalimentation I and the second one superalimentation II for a half
year. The mean daily increases in weight were recorded (in Dg.):
62
52
, 54
56
, 55
49
, 60
50
, 53
51
, 58
50
.
Determine 95% confidence interval estimate for  = 1 - 2.
b) At the significance level  = 5% test the hypothesis that both superalimentation
have the same effect on the piglets' increases in weight.
Problem 4
Two independent random samples are given. The first one is of size 10 and follows N(2; 1, 5).
The second sample is of size 5 and follows N(3; 4). Find the probability that the sample
mean of the first sample is less than the sample mean of the second sample.