Question

Problem Statement 7 Energy drink consumption has continued to gain in popularity since the 1997 debut of Red Bull, the current leader in the energy drink market. Given below are the exam scores and the number of 12-ounce energy drinks consumed within a week prior to the exam of 10 college students.

Exam Scores75928464648681617393Number of Drinks5324273010

Referring to Problem Statement 7, what is the sample covariance between the exam scores and the number of energy drinks consumed?

Referring to Problem Statement 7, what is the sample correlation coefficient between the exam scores and the number of energy drinks consumed

Answer 1

Given :  exam scores and the number of 12-ounce energy drinks consumed within a week prior to the exam of 10 college students

Exam Scores        75 92 84 64 64 86 81 61 73 93

Number of Drinks 5  3     2   4   2   7   3     0  1   0

To Find  : sample covariance between the exam scores and the number of energy drinks consumed

sample correlation coefficient between the exam scores and the number of energy drinks consumed

Solution:

x y  $x_i-\overline{x}$ $y_i-\overline{y}$       ($x_i-\overline{x}$)($y_i-\overline{y}$)

75 5 -2.3      2.3     -5.29

92 3 14.7     0.3     4.41

84 2 6.7     -0.7          -4.69

64 4 -13.3 1.3      -17.29

64 2 -13.3 -0.7          9.31

86 7 8.7     4.3          37.41

81 3 3.7       0.3           1.11

61 0 -16.3 -2.7            44.01

73 1 -4.3       -1.7            7.31

93 0 15.7      -2.7         -42.39

773  27               33.9

sample covariance  =  ∑  ($x_i-\overline{x}$)($y_i-\overline{y}$) / (n - 1)

n = 10

=> sample covariance  = 33.9 / 9   = 3.767

sample correlation coefficient =  Cov xy /  (σx . σy)

σx  = √∑( $x_i-\overline{x}$ )² /(n - 1)   ,  σy  = √∑($y_i-\overline{y}$  )² /(n - 1)   ,

∑( $x_i-\overline{x}$ )² = 137.79 ,  ∑($y_i-\overline{y}$  )² = 4.9

σx = 11.74  , σy  = 2.21

sample correlation coefficient =   Cov xy /  (σx . σy)  =

3.767 / (11.74 * 2.21) =  0.145  

Learn More:

If u+5x=6 and 3y+7v=20 and correlation coefficient between x and y is

brainly.in/question/360809

The coefficient of correlation between two variables X and Y is 0.64 ...

brainly.in/question/13244585

Show that the coefficient of correlation is the geometric mean of the ...

brainly.in/question/19022008

Answer 2

Answer:

Step-by-step explanation: