Question

1. The human resource director at Schultz Industries is interested in examining the effect of gender and employee classification on the annual dollar amount of dental claims for unmarried employees in the company. Employee classifications range from category 1 (production-line worker) to category 4 (upper-level management). The director decided to use three replicates for each of the eight treatment combinations, requiring annual claims from 24 different employees. Use the sample results (below) to test for the significance of the gender, employee classification, and interaction between gender and employee classification. Use a significance level of 0.05.

Employee Classification

	Category 1	Category 2	Category 3	Category 4
Male	190	135	260	310
Male	225	180	330	280
Male	200	100	350	240
Female	235	275	160	160
Female	200	310	205	110
Female	270	285	140	80

                        (Note 1: To conduct your hypothesis test for parts (A) and (B) in problem #1, you need to use the randomized block design procedure in Excel denoted by “ANOVA: Two factors without Replication”).

                        (Note 2: For problem #2, you will be using “ANOVA: Two factor with Replication” procedure and will be conducting three hypothesis tests. Please make sure to specify your null and alternative hypotheses for each case and write your conclusion in each case).

Answer 1

Problem #1:

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
Male	4	895	223.75	5922.917
Male	4	1015	253.75	4256.25
Male	4	890	222.5	10691.67
Female	4	830	207.5	3275
Female	4	825	206.25	6689.583
Female	4	775	193.75	9989.583
Category 1	6	1320	220	890
Category 2	6	1285	214.1667	7674.167
Category 3	6	1445	240.8333	7644.167
Category 4	6	1180	196.6667	8826.667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	8670.833	5	1734.167	0.223275	0.946781	2.901295
Columns	5970.833	3	1990.278	0.25625	0.855696	3.287382
Error	116504.2	15	7766.944
Total	131145.8	23

There is no significant effect of gender, employee classification, and interaction between gender and employee classification.

Problem #2:

Anova: Two-Factor With Replication
SUMMARY	Category 1	Category 2	Category 3	Category 4	Total
Male
Count	3	3	3	3	12
Sum	615	415	940	830	2800
Average	205	138.3333	313.3333	276.6667	233.3333
Variance	325	1608.333	2233.333	1233.333	5919.697
Female
Count	3	3	3	3	12
Sum	705	870	505	350	2430
Average	235	290	168.3333	116.6667	202.5
Variance	1225	325	1108.333	1633.333	5484.091
Total
Count	6	6	6	6
Sum	1320	1285	1445	1180
Average	220	214.1667	240.8333	196.6667
Variance	890	7674.167	7644.167	8826.667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	5704.167	1	5704.167	4.708512	0.045415	4.493998
Columns	5970.833	3	1990.278	1.642878	0.219138	3.238872
Interaction	100087.5	3	33362.5	27.53912	1.48E-06	3.238872
Within	19383.33	16	1211.458
Total	131145.8	23

There is a significant effect of gender, and interaction between gender and employee classification.

There is no significant effect of employee classification.