Degrees: Physiotherapy, Medicine
Date: November 28, 2016

## Question 1

The table below gives the distribution of points obtained by students in a physiotherapy public competition this year.

1. Compute the interquartile range and explain your result. Are there outliers in the sample?
2. The minimum number of points to pass the exam is 150; what percentage of students passed the exam?
3. If the mean of the score of the previous year exam was 80 points and the standard deviation was 52 points, which year is the mean more representative? Justify the answer.
4. According to the values of skewness and kurtosis, can we assume that the sample has been taken from a normally distributed population?
5. What score is relatively higher, 150 points in this year exam or 160 in the previous year exam? Justify the answer.

## Question 2

A study try to determine the relation between obesity and the response to pain. The obesity is measured as the percentage over the ideal weight ($X$), and the response to pain with a measure of the twinge sensation. For a sample of 10 individuals we got the following sums:

$\sum x_i=737$, $\sum y_j=77$, $\sum x_i^2=55589$, $\sum y_j^2=799.5$, $\sum x_iy_j=6056.5$

1. Compute the linear regression model of the response to pain on the obesity.
2. What is the change in the response to pain for an increment of one point in the weight?
3. What percentage of the variability of the response to pain does not explain the linear regression model?
4. Taking into account the parameters of the exponential model given in the table below, give the equation of the exponential model. Which transformation is required to convert this model into a linear one?
1. What is the expected response to pain for an obesity of 50\% according to the linear model? And according to the exponential model? Which prediction is more reliable?