There are three hospitals in the Tulsa, Oklahoma, area. The following data show
ID: 3073060 • Letter: T
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?
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.)
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 TotalExplanation / Answer
Solution:
1. Set up the null hypothesis and the alternate hypothesis.
Answer:
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: Ha: 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.)
Answer:
For treatment, we are given = 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 = 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.)
Answer:
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
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