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:
505,4 512,6 502,3 519,6 505,4 499,2 513,7 509,7 508,3 504,5 515,2 513,5 517,1501,4 503,5 516,9 499,6 503,7 506,9 513,4 509,2 507,0 521,2 505,8 506,3Propose 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) inkg, 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!
3. After a bit of thought, we say to ourselves that comparing weights is perhaps not the smartest thing. Remember that the body mass index BMI is calculated using the formula Without going into detail about your reasoning – but specifying what is changed – repeat the previous question to compare body mass indexes.
Exercise 3: Annoy the computer scientist! [4 points] An IT department feels that it is too often disturbed by trivial matters. It has recorded, during 4 quarters, the number of useless requests:
Quarter 1: 675; Quarter 2: 720; Quarter 3: 610; Quarter 4: 700.
Can we conclude, at the 95% confidence level, that there are as many applications each quarter?
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