Question

1. 4) Suppose you want to find out if there is a relationship between anxiety and sleep deprivation. So you go out and find 7 people and measure how much anxiety they are experiencing in their lives and how many hours of sleep they are getting.

   Let X be the explanatory variable to describe anxiety, you obtain the following values for X in order from subject 1 to subject 7: 1, 2, 4, 4, 5, 8, 7 Let Y be the response variable to describe the hours of sleep they are getting, you obtain the following values for
   Y in order from subject 1 to subject 7: 8, 5, 5, 5, 4, 2, 1

   1. a) Draw a precise scatter plot illustrating the data (15pts).

   2. b) Compute the means and standard deviations for the two sample

      distributions (10pts)

   3. c) Calculate the correlation coefficient ‘r’ that quantifies the relationship

      between the two variables. (30pts). Are the two variables positively or negatively correlated? (5pts). Based on the data, if you want to get more sleep, should you try to be more or less anxious? (5pts)

Answer 1

a ) The scatter diagram of Y vs. X is given below :

b ) Mean for X :

Standard deviation of X :

Mean for Y :

Standard deviation of Y :

c )

Based upon the scatter plot and the value of the correlation coefficient , we can say that the two variables are negatively correlated . Thus , based on the data , if one wants to get more sleep , he/she should try to be less anxious .