Question

Can an answer, complete with workings please be provided for Problem 32E, Chapter 15 from the Business Statistics: Communicating with Numbers (2nd Edition) be made available?

The manager of a local Costo store is in the process of making hiring decisions for selling mobile phone contracts. She believes that the sale of mobile phone contracts depends crucially on the number of hours clocked by male and female employees. She collects the weekly data on last year’s sales of mobile phone contracts (Sale) along with work hours of male (Hours Males) and female (Hours Females) employees. A portion of the data is shown in the accompanying table.

a.	Report the sample regression equation of the appropriate model.
b.	At the 5% significance level, are the explanatory variables jointly significant? Are they individually significant? Use the p-value approach for the tests.
c.	The manager would like to determine whether there is a difference in productivity of male and female employees. In other words, for the same work hours, whether the number of sales of mobile contracts varies between male and female employees. Conduct the appropriate test at the 5% level of significance. Provide the details. Sale Hours Males Hours Females 59 30 32 65 33 36 62 27 34 61 28 34 65 33 37 63 33 35 55 27 29 61 25 38 63 31 34 63 32 35 59 28 29 63 34 34 64 35 34 61 26 35 62 30 33 61 31 33 62 29 34 62 31 32 62 29 34 63 33 32 65 33 36 59 30 29 62 30 35 59 28 33 61 31 32 61 30 35 65 35 32 62 29 34 56 24 31 63 29 36 64 28 34 59 29 33 63 27 36 61 30 35 64 32 35 62 29 34 56 26 32 63 29 35 63 27 37 63 32 34 64 28 38 59 24 33 61 28 35 64 31 34 64 32 36 65 31 35 62 28 36 63 33 34 65 32 36 61 29 36 61 30 34 64 35 35

Answer 1

a)

Here i write R-code for given problem as:

s=c(59,65,62,61,65,63,55,61,63,63,59,63,64,61,62,61,62,62,62,63,65,59,62,59,61,61,65,62,56,63,64,59,63,61,64,62,56,63,63,63,64,59,61,64,64,65,62,63,65,61,61,64)
m=c(30,33,27,28,33,33,27,25,31,32,28,34,35,26,30,31,29,31,29,33,33,30,30,28,31,30,35,29,24,29,28,29,27,30,32,29,26,29,27,32,28,24,28,31,32,31,28,33,32,29,30,25)
f=c(32,36,34,34,37,35,29,28,34,35,29,34,34,35,33,33,34,32,34,32,36,29,35,33,32,35,32,34,31,36,34,33,36,35,35,34,32,35,37,34,38,33,35,34,36,35,36,34,36,36,34,35)
d=data.frame(s,m,f)
d
a=aov(s~f+m+f*m,d)
summary(a)

And the output is;

summary(a)
Df Sum Sq Mean Sq F value Pr(>F)   
f 1 114.41 114.41 52.692 2.95e-09 ***
m 1 59.04 59.04 27.192 3.87e-06 ***
f:m 1 0.01 0.01 0.005 0.944   
Residuals 48 104.23 2.17
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

b)

Here both p-values are less than 0.05, thus the explainitory variable is jointly significant.
And the interaction effect is insignificant.

c)

H0: Their is no difference in productivity of male and female employee.
H1: Their is difference in productivity of male and female employee.

Here the R-code is as follows;

m=c(30,33,27,28,33,33,27,25,31,32,28,34,35,26,30,31,29,31,29,33,33,30,30,28,31,30,35,29,24,29,28,29,27,30,32,29,26,29,27,32,28,24,28,31,32,31,28,33,32,29,30,25)
f=c(32,36,34,34,37,35,29,28,34,35,29,34,34,35,33,33,34,32,34,32,36,29,35,33,32,35,32,34,31,36,34,33,36,35,35,34,32,35,37,34,38,33,35,34,36,35,36,34,36,36,34,35)
t.test(m,f)

And the output is,

Welch Two Sample t-test

data: m and f
t = -8.9488, df = 96.51, p-value = 2.59e-14
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-5.169160 -3.292378
sample estimates:
mean of x mean of y
29.69231 33.92308

Here, p-value is less than 0.05, thus we reject H0 at 5% l.o.s.