Question

There are three hospitals in the Tulsa, Oklahoma, area. The following data show the number of outpatient surgeries performed on Monday, Tuesday, Wednesday, Thursday, and Friday at each hospital last week. At the 0.01 significance level, can we conclude there is a difference in the mean number of surgeries performed by hospital or by day of the week?

	Number of Surgeries Performed
Day	St. Luke's	St. Vincent	Mercy
Monday	30	45	34
Tuesday	12	16	12
Wednesday	31	28	23
Thursday	11	14	13
Friday	20	32	25
1. Set up the null hypothesis and the alternate hypothesis. 2. State the decision rule for 0.01 significance level. (Round your answers to 2 decimal places.) For Treatment: Reject H0 if F > ________ For blocks: Reject H0 if F > ________ 3. Complete the ANOVA table. (Round your SS, MS and F to 2 decimal places.) Source SS df MS F Treatments Blocks Error Total

Answer 1

Solution:

1. Set up the null hypothesis and the alternate hypothesis.

Null hypothesis: H₀: There is no any statistically significant difference in the mean number of surgeries performed by hospital or by day of the week.

Alternative hypothesis: H_a: There is a statistically significant difference in the mean number of surgeries performed by hospital or by day of the week.

2. State the decision rule for 0.01 significance level. (Round your answers to 2 decimal places.)

For treatment, we are given α = 0.01, df1 = 2, df2 = 8, so by using F-table or excel, F critical value = 8.649111

For Treatment: Reject H0 if F > 8.65

For blocks, we are given α = 0.01, df1 = 4, df2 = 8, so by using F-table or excel, F critical value = 7.006077

For blocks: Reject H0 if F > 7.01

3. Complete the ANOVA table. (Round your SS, MS and F to 2 decimal places.)

Required

Required ANOVA table by using Excel is given as below:

MS = SS/df

F for treatment= MST/MSE

F for block = MSB/MSE

Source	SS	df	MS	F	F-critical	P-value
Treatments	116.93	2	58.47	3.76	8.65	0.07
Blocks	1211.60	4	302.90	19.48	7.01	0.00
Error	124.40	8	15.55
Total	1452.93	14