11. seminar
Problem 1
The score of two subjects of eight randomly drawn students are recorded.
1 2 3 4 5 6 7 8
80 50 36 58 42 60 56 68
65 60 35 39 48 44 48 61
At the significance level 0.05 carry out the test that the results in considered two subjects
are not positively correlated.
Problem 2
A ferrum content was determined in an iron ore sample of size 600 by two analytic methods,
where the sample correlation coefficient was R12 = 0, 85. A technical literature states that
the correlation coefficient between considered methods is = 0, 9. At the significance level
0.05 carry out a test H0 : = 0, 9 against H1 : = 0, 9.
Problem 3
An officer of human resources department of particular firm is interested in a relationship
between a number of absence days due to illness per year (variable Y ) and age of employee
(variable X). Therefore the data about 10 employees were drawn randomly.
1 2 3 4 5 6 7 8 9 10
27 61 37 23 46 58 29 36 64 40
15 6 10 18 9 7 14 11 5 8
Under the assumption that X
Y
follows bivariate normal distribution do following tasks:
a) Calculate sample correlation coefficient.
b) At the significance level 0.05 carry out a test that X and Y are independent.
c) Determine the 95% confidence interval for correlation coefficient .
Problem 4
A medical research observed the concentration of substances A and B in urine of patients
with particular kidney illness. In a sample of 100 healthy individuals the sample correlation
coefficient between concentration of A and B was 0,65. In a sample of 142 individuals with
mentioned kidney illness the sample correlation coefficient was 0,37. At the significance
level 0.05 test the hypothesis that the true correlation coefficients are equal.
Problem 5
in supplement