Question

A business manager wanted to know if there was a relationship between daily temperature measured in degrees Fahrenheit and number of employees who called-in sick each day. He collected the following data over 10 days:

Daily Temperature: 64 60 67 63 60 64 72 66 60 69

# Called-in Sick: 33 32 30 37 34 28 31 27 31 26

a. Find the value of the correlation coefficient (r) for Daily Temperature and # Called-in Sick.

b. What does the null hypothesis expect for the problem described. (Be sure to use the variables given in the problem.)

c. Conduct a statistical test of the null hypothesis using p = .05. Be sure to properly state your statistical conclusion.

d. Provide an interpretation of your statistical conclusion given in part C.

e. What is the value of the coefficient of determination?

f. Provide an interpretation of your answer to Part E.

Answer 1

I used R software to solve this question.

R codes and output:

> temp=c(64, 60, 67, 63, 60, 64, 72, 66, 60, 69)
> call=c(33, 32, 30, 37, 34, 28, 31, 27, 31, 26)
> cor.test(temp,call)

Pearson's product-moment correlation

data: temp and call
t = -1.505, df = 8, p-value = 0.1707
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.8484337 0.2270321
sample estimates:
cor
-0.4697416

a.

Correlation coefficient = r = -0.4697416

b.

Hypothesis:

c.

P-value for testing this hypothesis is 0.1707 which is greater than 0.05, hence we accept null hypothesis and conclude that correlation between temperature and called -in sick is not statistically significant.

e.

Coefficient of determination = r2 = ( -0.4697 )2 = 0.2206

f.

It means temperature will explain 22.06% variation in the Called-in Sick.