In 2015 the Washington State Department of Health recorded the number of men and
ID: 2924146 • Letter: I
Question
In 2015 the Washington State Department of Health recorded the number of men and women age 25-34 to die of the following causes:
malignant
neoplasms
heart
disease
In order to improve Health and Safety targets, we would like to know whether the probability of each cause of death is the same for men and women. (Data from Washington State Department of Health, https://www.doh.wa.gov/).
H0 : The variables gender and cause of death are not related
H1 : The variables gender and cause of death are related
a.) If the probability of each cause of death is the same for men and women, how many women would we expect to die as a result of homicide?
b.) What conclusions would you draw about the hypothesis test? State your conclusion both statistically, and in a non-technical way that could be communicated to the general public.
Cause of Death accident suicide homicidemalignant
neoplasms
heart
disease
other total male 113 67 28 13 8 35 264 female 39 13 6 6 3 21 88 total 152 80 34 19 11 56 352Explanation / Answer
Here, we have to use Chi square test for checking whether the two categorical variables are related or not. The test statistic formula is given as below:
Chi square = [(O – E)/E]
Where, O is observed frequency and E is expected frequency.
Expected frequency is given as below:
Expected frequency = E = Row total * Column total / Grand total
a.) If the probability of each cause of death is the same for men and women, how many women would we expect to die as a result of homicide?
Solution:
Expected number of women = Row total * Column total / Grand total
Expected number of women = 88*34/352 = 8.5
Expected number of women = 9 approximately (rounded)
b.) What conclusions would you draw about the hypothesis test? State your conclusion both statistically, and in a non-technical way that could be communicated to the general public.
Solution:
For the given chi square test of independence, the p-value is given as 0.09351882 which is greater than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis that the variables gender and cause of death are not related. There is insufficient evidence to conclude that the cause of death is related to the gender of the person. There is sufficient evidence to conclude that the cause of death is not related to the gender of the person. There is no any relationship found in the cause of death and gender of the person.
The excel output for this Chi square test is given as below:
Chi-Square Test
Observed Frequencies
Column variable
Row variable
C1
C2
C3
C4
C5
C6
Total
R1
113
67
28
13
8
35
264
R2
39
13
6
6
3
21
88
Total
152
80
34
19
11
56
352
Expected Frequencies
Column variable
Row variable
C1
C2
C3
C4
C5
C6
Total
R1
114
60
25.5
14.25
8.25
42
264
R2
38
20
8.5
4.75
2.75
14
88
Total
152
80
34
19
11
56
352
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
6
Degrees of Freedom
5
Results
Critical Value
11.0705
Chi-Square Test Statistic
9.417713
p-Value
0.093519
Do not reject the null hypothesis
Expected frequency assumption
is met.
Chi-Square Test
Observed Frequencies
Column variable
Row variable
C1
C2
C3
C4
C5
C6
Total
R1
113
67
28
13
8
35
264
R2
39
13
6
6
3
21
88
Total
152
80
34
19
11
56
352
Expected Frequencies
Column variable
Row variable
C1
C2
C3
C4
C5
C6
Total
R1
114
60
25.5
14.25
8.25
42
264
R2
38
20
8.5
4.75
2.75
14
88
Total
152
80
34
19
11
56
352
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.