Homework SourseThe data on the Hospital Stay worksheet of Chpt 81xls show a
The data on the Hospital Stay worksheet of Chpt 8-1.xls show a sample of one hundred hospital stays by Sex and LOS. Stays >3 days are coded as Long; those 3 days or less are coded Short.
a. Use the pivot table capability of Excel and the chi-square to test the hypothesis of independence between Sex and Stay as coded Long or Short.
b. Use conditional probabilities to provide an interpretation of the results.
| Sex | LOS | Stay |
| F | 4 | Long |
| F | 8 | Long |
| F | 10 | Long |
| M | 5 | Long |
| F | 3 | Short |
| F | 2 | Short |
| F | 5 | Long |
| M | 6 | Long |
| M | 6 | Long |
| F | 14 | Long |
| F | 11 | Long |
| M | 5 | Long |
| M | 6 | Long |
| F | 3 | Short |
| M | 3 | Short |
| F | 7 | Long |
| F | 6 | Long |
| F | 3 | Short |
| F | 11 | Long |
| F | 2 | Short |
| F | 2 | Short |
| F | 2 | Short |
| M | 7 | Long |
| F | 4 | Long |
| F | 10 | Long |
| F | 6 | Long |
| F | 3 | Short |
| F | 6 | Long |
| F | 6 | Long |
| M | 1 | Short |
| M | 3 | Short |
| F | 3 | Short |
| F | 5 | Long |
| M | 5 | Long |
| M | 3 | Short |
| M | 2 | Short |
| F | 6 | Long |
| M | 1 | Short |
| F | 10 | Long |
| F | 2 | Short |
| F | 2 | Short |
| F | 2 | Short |
| F | 3 | Short |
| M | 2 | Short |
| F | 6 | Long |
| F | 4 | Long |
| F | 10 | Long |
| F | 7 | Long |
| F | 4 | Long |
| F | 1 | Short |
| M | 2 | Short |
| F | 9 | Long |
| M | 2 | Short |
| F | 3 | Short |
| M | 4 | Long |
| F | 2 | Short |
| M | 1 | Short |
| F | 5 | Long |
| M | 12 | Long |
| F | 7 | Long |
| F | 4 | Long |
| M | 4 | Long |
| F | 1 | Short |
| F | 7 | Long |
| F | 2 | Short |
| F | 4 | Long |
| F | 14 | Long |
| F | 1 | Short |
| M | 10 | Long |
| F | 2 | Short |
| M | 1 | Short |
| M | 2 | Short |
| F | 10 | Long |
| F | 3 | Short |
| F | 7 | Long |
| M | 2 | Short |
| M | 9 | Long |
| M | 3 | Short |
| M | 3 | Short |
| F | 2 | Short |
| M | 11 | Long |
| F | 16 | Long |
| F | 3 | Short |
| M | 5 | Long |
| F | 1 | Short |
| F | 8 | Long |
| M | 5 | Long |
| F | 2 | Short |
| F | 10 | Long |
| M | 9 | Long |
| F | 7 | Long |
| F | 4 | Long |
| M | 5 | Long |
| F | 2 | Short |
| F | 5 | Long |
| F | 3 | Short |
| M | 7 | Long |
| M | 9 | Long |
| M | 7 | Long |
| M | 5 | Long |
Solution
The data on the Hospital Stay worksheet of Chpt 8-1.xls show a sample of one hundred hospital stays by Sex and LOS. Stays >3 days are coded as Long; those 3 days or less are coded Short.
Null hypothesis:Sex and Stay are independent
Alternate hypothesis:Sex and Stay are not independent
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
Long
Short
Total
fo-fe
F
37
27
64
-0.1200
0.1200
M
21
15
36
0.1200
-0.1200
Total
58
42
100
Expected Frequencies
Column variable
Row variable
Long
Short
Total
(fo-fe)^2/fe
F
37.12
26.88
64
0.0004
0.0005
M
20.88
15.12
36
0.0007
0.0010
Total
58
42
100
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
2
Degrees of Freedom
1
Results
Critical Value
3.841
Chi-Square Test Statistic
0.0026
p-Value
0.9596
Do not reject the null hypothesis
Calculated chi square =0.0026 < 3.841 the table value at 0.05 level.
The null hypothesis is not rejected
We conclude that Sex and Stay are independent.
b. Use conditional probabilities to provide an interpretation of the results.
Column probabilities
Long
Short
F
0.6379
0.6429
M
0.3621
0.3571
1
1
From the above table probability, it is almost same for long term stay and short term stay for Females and males.
| Chi-Square Test | ||||||
| Observed Frequencies | ||||||
| Column variable | Calculations | |||||
| Row variable | Long | Short | Total | fo-fe | ||
| F | 37 | 27 | 64 | -0.1200 | 0.1200 | |
| M | 21 | 15 | 36 | 0.1200 | -0.1200 | |
| Total | 58 | 42 | 100 | |||
| Expected Frequencies | ||||||
| Column variable | ||||||
| Row variable | Long | Short | Total | (fo-fe)^2/fe | ||
| F | 37.12 | 26.88 | 64 | 0.0004 | 0.0005 | |
| M | 20.88 | 15.12 | 36 | 0.0007 | 0.0010 | |
| Total | 58 | 42 | 100 | |||
| Data | ||||||
| Level of Significance | 0.05 | |||||
| Number of Rows | 2 | |||||
| Number of Columns | 2 | |||||
| Degrees of Freedom | 1 | |||||
| Results | ||||||
| Critical Value | 3.841 | |||||
| Chi-Square Test Statistic | 0.0026 | |||||
| p-Value | 0.9596 | |||||
| Do not reject the null hypothesis |
