For each exercise, you will specify:

_ the random variable(s) introduced ;
_ whenever necessary, the test performed by explaining H0 and H1 ;
_ the assumptions needed to perform the test ;
_ the conclusion of the test, mentioning the corresponding risk.

Exercise 1: First contentful paint [6 points]

According to the specifications imposed on the website designer, the first text or image must
be displayed in 510ms.

The results (in ms) of 25 queries are as follows:

505,4 512,6 502,3 519,6 505,4 499,2 513,7 509,7 508,3 504,5 515,2 513,5 517,1
501,4 503,5 516,9 499,6 503,7 506,9 513,4 509,2 507,0 521,2 505,8 506,3

Propose a test procedure to check if the site meets the specifications and implement it.
(Several possibilities are possible).

Exercise 2: Weights and heights of children [10 points].

The file Enfants.txt contains 151 records from medical examinations of children in their first
year of kindergarten in a French town in 1996. It contains, for each child:

_ its sex, coded in the variable SEX by F for girl and G for boy ;
_ its weight (actually mass) in kg, in the variable weight ;
_ its height in cm, in the variable height ;
_ its age in years and months, in the variables year and month ;

The fact that her school is located in a priority education zone, coded in the zep variable by
Y for yes and N for no.

1. Import the file Children.txt.

2. (a) Define a vector x1 containing the weights of children whose school is in a priority
education zone
and a vector y1 containing the weights of children whose school is not in a priority
education zone.

(b) Can we consider, at the 95% level of confidence, that the weights of children at schools
in priority zones are identical to those of children at schools outside priority zones?
We will implement a test procedure, remembering to carry out all the intermediate
tests!