Degrees: Pharmacy, Biotechnology
Date: October 29, 2018

Question 1

A study about obesity in a city has measured the body mass index (BMI) in a sample. The collected data is shown in the table below.

1. Compute the percentage of people with a BMI between 19 and 25.
2. Which is the BMI with a 20% of persons above it?
3. Are there outliers in the sample? Give the outliers if there are some.

Question 2

A gene of a rat species has been modified to help the metabolization of cholesterol in blood. To check the effectiveness of this genetic modification two samples of rats were drawn, ones with the gene modified and the others not, and they were fed with the same diet with different concentrations of palm oil during one month. The following sums summarize the results:

Palm oil quantity in gr (the same in both samples)
$\sum x_i=640.6467$ gr, $\sum x_i^2=23508.6387$ gr², $\sum(x_i-\bar x)^3=-5527.08$ gr³, $\sum(x_i-\bar x)^4=792910$ gr⁴
Cholesterol level in blood in mg/dl of non genetically modified rats $\sum y_j=2945.8545$ mg/dl, $\sum y_j^2=439517.5975$ (mg/dl)², $\sum(y_j-\bar y)^3=604.08$ (mg/dl)³, $\sum(y_j-\bar y)^4=3717331.07$ (mg/dl)⁴
$\sum x_iy_j=98156.0658$ gr$\cdot$mg/dl.
Cholesterol level in blood in mg/dl of genetically modified rats
$\sum y_j=2126.5899$ mg/dl, $\sum y_j^2=226824.5373$ (mg/dl)², $\sum(y_j-\bar y)^3=-629.4$ (mg/dl)³, $\sum(y_j-\bar y)^4=48248.29$ (mg/dl)⁴ $\sum x_iy_j=69517.3648$ gr$\cdot$mg/dl.

1. In which sample the cholesterol has a more representative mean, genetically modified or non modified rats?
2. In which sample the distribution of cholesterol is more skew?
3. In which sample the kurtosis of the distribution of cholesterol is less normal?
4. Which rat has a cholesterol level relatively bigger, a genetically modified rat with a cholesterol level of 130 mg/dl, or a non genetically modified rat with a cholesterol level of 145 mg/dl?
5. In which sample the regression line of cholesterol on the palm oil quantity fits better?
6. According to the regression line, what level of cholesterol is expected for a genetically modified rat with a diet of 25 gr of palm oil? And for a non genetically modified rat?
7. What amount of palm oil must be supplied to a non genetically modified rat to have a cholesterol level smaller than 150 mg/dl? Is this prediction reliable?

Question 3

It is known that the regression line of $Y$ on $X$ has equation $3x+2y-4=0$ and it explains half of the variability of $Y$. According to the linear regression model, how much will $X$ change for each unit that increases $Y$?