6. seminar
Problem 1
6 equally-old piglets were drawn randomly from a population of a particular race and
they had been served superalimentation (fattening diet) for a half year. For any piglet the
mean daily increases in weight were recorded (in Dg.): 62, 54, 55, 60, 53, 58. We know
from previous experiments that weight increases follow the normal distribution. At the
significance level  = 0.05 find
a) the lower estimate for the unknown expected value 
b) the interval estimate for the standard deviation .
Problem 2
A dairy wishes to keep up an upper bound for a variance of a fat content in its milk (in
percentages). If the assumed fat content is % then the fat content in a particular milk
bottle should not deviate from this value too much. For the dairy the standard deviation
at most  = 0.1% of the fat content is acceptable. 20 milk bottles were drawn randomly
and we have measured out the following percentage values of the fat content:
1.83; 2.22; 1.98; 1.88; 1.95; 1.78; 2.03; 2.23; 1.63; 1.84; 2.00; 2.07; 2.02; 2.05; 2.12; 1.91;
2.06; 2.15; 1.89; 1.91. We assume the milk fat content to be normally distributed.
a) At  = 0.05 run a test H0 :   0.1 versus H1 :  > 0.1. Use a classical method.
b) Run the same test using an interval method.
c) If X denotes the milk fat content find the probability:
P(|X - | > )
P(|X - | > 3)
Problem 3
It is known that the tallness of boys in age 9,5 to 10 years follows the normal distribution.
A pediatrician drawn randomly 15 boys of considered age and calculated the sample mean
value m = 139, 13cm and the sample standard deviation value s2
= 39, 2cm2
. According
to his opinion the tallness should not exceed 142 cm. Can we accept the pediatrician's
assertion? (At  = 0.05.) Use both classical testing method and interval testing method.
Problem 4
6 new cars of particular brand were drawn randomly and after some period the differences
between front left tyre and front right tyre abrasion were recorded: 0.3, -0.1, 0.2, -0.2, 0.1,
0.2. We assume that the both random variables giving the attrition of the left or the right
tyre are normally distributed. At the confidence level 90% decide if the abrasions of the
front tyres are equal.