3) A researcher wonders if there is a correlation between visual acuity (measured on a scale of 1 to 10, where 10 represents better vision) and the number of accidents. It draws a random sample and obtains the following results:

Acuit visuelle

Nombre d'accidents

2

6

3

6

3

5

6

4

7

4

8

3

9

4

9

3

a. Calculate the Pearson correlation.

b. Perform the hypothesis test at the 0.05 level by making the necessary calculations.

c. Check these calculations using the SPSS software.

d. Interpret your results.

4) A researcher wonders if the weight of mice varies depending on the amount of food they are given. It obtains the following results:

Souris

Poids en grammes

Nourriture en grammes

1

72

15

2

88

19

3

76

16

4

82

18

5

66

13

6

69

14

7

79

17

8

90

21

9

92

23

10

95

25

5. Make the necessary calculations to answer the following questions.

at. (10.5 points)

What is the regression equation?

b. (3.5 points)

What is the variation error?

vs. (3.5 points)

What is the variation explained?

d. (3.5 points)

What is the total variation?

e. (3.5 points)

What is the variance explained?

f. (3.5 points)

Using the regression equation, calculate the weight you would expect from a mouse if it is given 22 grams of food per day.

6. (7 points)

For a sample of 40 students, we have the number of hours of weekly study and the average of the academic results at the end of the year. Referring to the results generated by the SPSS software which are transcribed below, interpret this relationship between the two variables.