1. A company would like to evaluate the time in years, that an employee spent at

ID: 3370042 • Letter: 1

Question

1. A company would like to evaluate the time in years, that an employee spent at a company and the employee’s hourly pay, for 5 employees are listed in the table below. Calculate and interpret the correlation coefficient r. Include a plot of the data in your discussion.:

Years (X)

Hourly Pay (Y)

a. Calculate the Pearson correlation coefficient for this set of data.

b. Use an appropriate 2-tailed hypothesis test (? = .05) to determine whether this relationship is statistically significant.

c. Based on your calculations, what can we conclude about the relationship between hours worked and hourly pay?

Years (X)

Hourly Pay (Y)

Explanation / Answer

Solution

Back-up Theory

Correlation Coefficient of X and Y = rXY= Sxy/sq.rt(Sxx.Syy). ………………(1), where

Sxy = sum of {(xi – Xbar)(yi – Ybar)} over i = 1, 2, …., n………………….…(2)

Sxx = sum of (xi – Xbar)2 over i = 1, 2, …., n …………………………….…..(3)

Syy = sum of (yi – Ybar)2 over i = 1, 2, …., n …………………………………(4)

Xbar = (1/n)sum of xi over I = 1, 2, …., n; …………………………………….(5)

Ybar =(1/n)sum of yi over i= 1, 2, …., n;……………………………..……….(6)

To test for significance of correlation coefficient

t = r?{(n - 2)/(1 – r2)} asymptotically ~ tn – 2 …………………………………(7)

Part (a)

Xbar

7.40

ybar

27.8

Sxx

101.2

Syy

270.8

Sxy

160.4

0.9689

ANSWER

Part (b)

Test for significance of r

t = r?{(n - 2)/(1 - r2)}

1- r^2

0.0612

(n-2)/(1-r^2)

49.0308

sqrt

7.0022

tcal

6.7846

tcrit

3.1824

p-value

0.0065

Since tcal > tcrit and also p-value < 0.05, the null hypothesis of no correlation is rejected.

=> the correlation coefficient is significant. ANSWER

Part (c)

The correlation coefficient is significant => there is sufficient evidence to suggest that the time the employee is with the company and the employee’s pay are related. ANSWER