Statistical Methods for Economists – Week 2

                                       (Questions and Tasks)

The topic: Hypothesis testing

1.) Explain what is a statistical hypothesis, and what is a null hypothesis.

2.) Explain what is a statistical significance and p-value.

3.) What 4 main steps are involved when testing a hypothesis?

4.) Explain the difference between a parametric and a non-parametric test.

5.) (One-sample t-test for the population mean) Test the hypothesis that an average bank loan is
25 000 Euro in a certain bank, if the sample of bank loans (obtained randomly) is: 30 000; 15 000;
22 000; 50 000; 20 000; 18 000; 15 000; 30 000 Euro.

6.) (Two-sample t-test of pop. means with equal variances) Test the hypothesis that the consumption
of salt and sugar per month in ten randomly chosen households is the same.

household no.

                                                              1

                                                                                                    2

                                                                                                       3

                                                                                                          4

                                                                                                             5

                                                                                                                6

                                                                                                                   7

                                                                                                                      8

                                                                                                                         9

                                                                                                                           10

salt (kg)

                                                             1.5

                                                                                                   2.2

                                                                                                      4.0

                                                                                                         3.6

                                                                                                            2.2

                                                                                                               2.8

                                                                                                                  1.7

                                                                                                                     2.3

                                                                                                                        3.5

                                                                                                                           2.8

sugar (kg)

                                                             3.3

                                                                                                   4.1

                                                                                                      2.7

                                                                                                         3.5

                                                                                                            3.6

                                                                                                               2.8

                                                                                                                  3.9

                                                                                                                     2.5

                                                                                                                        2.4

                                                                                                                           3.8


7.) Use F-test to test the hypothesis about equality of variances (salt vs sugar) in the previous
Problem 6.

8.) Explain how Chi-test is used for testing hypothesis.

9.) (Chi-square test) In the table below there is a statistics of car crashes in a town X. Test the
hypothesis that the number of crashes in each month is the same.

                                               Month

                                                                                                     January

                                                                                                           February

                                                                                                                     March

                                                                                                                          April

                                            Car crashes

                                                                                                       15

                                                                                                              22

                                                                                                                      17

                                                                                                                           24

10.) (Chi-square test) In the table below there are numbers of men and women visiting (or not)
local wellness (based on a random sample). Test the hypothesis that women and men visit the
wellness equally.


                                                    visit wellness

                                                                                                             do not visit

                                                Men

                                                                                                    50

                                                                                                                  54

                                               Women

                                                                                                    68

                                                                                                                  48