Exercise sheet
Statistical inference
Fabio Di Nocera
AY 2024/2025
Exercise 1. An athlete wants to see if their time is better that the time of a competitor on 5 km runs. They carefully record all of their times on 5 km runs in the
last month.
Run
1
2
3
4
5
6
7
8
Time (s)
857
832
838
843
845
852
831
864
The reference value that they take for their competitor is 835 s. Use a t-test to see
if their performance is better than their competitor’s performance, with a
confidence level of 5%.
1
Exercise 2. A researcher wants to compare the effectiveness of two different teaching
methods (Method A and Method B) on student performance. They select 10 pairs of
students, matching them based on similar academic backgrounds and abilities. Each
pair has one student taught using Method A and the other using Method B. The test
scores of the students are recorded as follows:
Pair
1
2
3
4
5
6
7
8
9
10
Student (Method A)
85
78
90
70
75
88
82
76
85
90
Student (Method B)
88
82
92
68
80
90
85
78
87
93
Use a paired t-test to see if Method B gives better results, with a confidence level of
5%.
Exercise 3. You are a market researcher studying the relationship between the type
of store where customers shop and their preferred payment method.
Variable A (Type of Store):
ˆ Grocery Store;
ˆ Electronics Store;
ˆ Clothing Store;
ˆ Furniture Store.
Variable B (Preferred Payment Method):
ˆ Cash;
ˆ Credit Card;
ˆ Mobile Payment.
You surveyed 300 customers and recorded their preferences in the following table.
Cash
Credit Card
Mobile Payment
Total
Grocery Store
30
40
30
100
Electronics Store
10
60
30
100
Clothing Store
25
40
15
80
Furniture Store
5
10
5
20
Use a χ2 -test for testing the independence hypothesis on these variables.
Total
70
150
80
300