Question

One of the local hospitals wants to assure that they have enough nurses for incoming patients needing assistance, especially in the emergency room. To insure there are enough nurses on duty, but not an overage which would waste hospital resources, the following data regarding the number of patients entering the hospital over the last several weeks has been gathered. The data does not include weekend patient traffic, as the hospital has previously done a similar study and staffed weekends appropriately. You are to analyze the data using ANOVA methodology and determine if there are any differences in the number of patients served by the day of the week. If you find there are differences, which days seem to be the busiest? You are to write a report to the hospital nursing manager of your findings. Be sure to include the problem statement (what you were asked to do), your analysis (include the statistical methodology used with graphs, charts, formulas, etc.), and your findings, along with a recommendation for staffing. Report length: 4-6 pages DATE DAY #PATIENTS 10/30/14 Monday 38 10/31/14 Tuesday 29 11/1/14 Wednesday 28 11/2/14 Thursday 30 11/3/14 Friday 36 11/6/14 Monday 29 11/7/14 Tuesday 25 11/8/14 Wednesday 23 11/9/14 Thursday 26 11/10/14 Friday 36 11/13/14 Monday 38 11/14/14 Tuesday 29 11/15/14 Wednesday 24 11/16/14 Thursday 20 11/17/14 Friday 33 11/20/14 Monday 28 11/21/14 Tuesday 29 11/22/14 Wednesday 28 11/23/14 Thursday 25 11/24/14 Friday 34 You will need to create your own Excel sheet using the data above in order to run the ANOVA calculation. To help aid in what should be in your first Case Study, you can use this as a quick checklist of the most important things. This isn't all inclusive as you are expected to write out what you did, why you did it and explain your logic. - hypothesis and null hypothesis - ANOVA - a follow-up statistical test/s to show where the differences are occurring - graphs/charts/tables referencing your analyses and findings - results as well as what we can conclude and what the next steps/decisions of the hospital should be

Answer 1

Model

Y_ij= μ+α_i+ε_ij, i = 1,2,3,4,5,j=1,2,3,4

Null Hypothesis

H₀: There is no significant differences in the number of patients served by the day of the week.

H₁: There is at least one day which has different number of patients served from other days.

Test Statistic F₀ = MS(days)/MSE

SSE = TSS-SS(Days)

Test Criteria : Reject H0 at alpha level of significance if F_cal> F_α[3,16]

	1	2	3	4	Ti.	Ti.2	ti.2/4
Monday	38	29	38	28	133	17689	4422.25
Tuesday	29	25	29	29	112	12544	3136
Wednesday	28	23	24	28	103	10609	2652.25
Thursday	30	26	20	25	101	10201	2550.25
Friday	36	36	33	34	139	19321	4830.25

GT	588
SS(days)	303.8
SSE	181
TSS	484.8

ANOVA TABLE
SV	DF	SS	MS	F RATIO
Between days	3	303.8	101.2667	8.95175
Error	16	181	11.3125
Total	19	484.8

F α[3,16]

3.12735

Since Calulate F_cal> F_α[3,16] , hence we reject H0.

Now we will perform pair wise comparison

H₀ : There is no significant difference between ith and jth day (i is not equal to j)

H₁: There is significant difference between ith and jth day (i is not equal to j)

Test statistic:

Reject Ho. If t₀ > tα/2(16)

or

Multiple Comparisons
Difference Table
(I) Day	(J) Day	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
					Lower Bound	Upper Bound
1	2	5.25000*	2.45628	.049	.0146	10.4854
1	3	7.50000*	2.45628	.008	2.2646	12.7354
1	4	8.00000*	2.45628	.005	2.7646	13.2354
1	5	-1.50000	2.45628	.551	-6.7354	3.7354
2	3	2.25000	2.45628	.374	-2.9854	7.4854
2	4	2.75000	2.45628	.281	-2.4854	7.9854
2	5	-6.75000*	2.45628	.015	-11.9854	-1.5146
3	4	.50000	2.45628	.841	-4.7354	5.7354
4	5	-9.00000*	2.45628	.002	-14.2354	-3.7646
*. The mean difference is significant at the 0.05 level.

Since day 1 is significant from all other days hence Monday seem to be the busiest.