Question

(3) A family owns a restaurant that has two locations: one in the town of Rabbit Hash, Kentucky and the other in the town of Deer Lick, Kentucky. The owners of the restaurants want to know if there is a difference in the tenure of their employees (how long an employee works there from hiring to quitting / firing) between the two locations. They collect the following data on the tenure of six recent employees. The data is the number of years the employee worked at that location.

Rabbit Hash, KY location	Deer Lick, KY location
9.1	3.8
3.7	12.1
0.1	5.2
1.1	5.1
0.3	4.8
0.5	5.0

• (a) Make a Q-Q plot for the Rabit Hash location.
• (b) Estimate a 95% confidence interval for the difference in the median tenure between the two locations.
• (c) Using the Wilcoxon Rank Sum Test, determine if there is a difference in the tenure between the two locations. Use a fixed type I error rate of 0.10.
• (d) What is the level of significance of the test that you conducted in part (c).

Answer 1

## R command

Rabbit_Hash=c(9.1,3.7,0.1,1.1,0.3,0.5)
Deer_Lick=c(3.8,12.1,5.2,5.1,4.8,5)

## a)
boxplot(Rabbit_Hash, Deer_Lick,
names=c("Rabbit Hash", "Deer Lick") )

## b)
t.test(Rabbit_Hash, Deer_Lick)

## c)
wilcox.test(x=Rabbit_Hash, y=Deer_Lick, alternative = "two.sided")

## End command

(a) Make a Q-Q plot for the Rabit Hash location.

The boxplot of Rabit Hash's location is the left side. From this box plot, we can see that the observation includes one outlier.

(b) Estimate a 95% confidence interval for the difference in the mean tenure between the two locations is (-7.7630938 0.6964272). It includes the value zero. Hence, there is no difference in the tenure of their employees at the 0.05 level of significance.

c) Using the Wilcoxon Rank Sum Test, determine if there is a difference in the tenure between the two locations. Use a fixed type I error rate of 0.10.

The p-value for the Wilcoxon Rank Sum Test statistic W = 5 is 0.04113. The p-value is smaller than 0.10. Hence, we can conclude that two locations have significantly different medians in the tenure of their employees at the 0.05 level of significance

d) What is the level of significance of the test that you conducted in part (c).

Ans: The level of significance of the test that you conducted in part is 0.10.