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In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in table E ("Global health observatory," 2013)
In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in table E ("Global health observatory," 2013): Expert Solutions for Success
In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in table E ("Global health observatory," 2013). In addition, the proportion of deaths of females from all causes for the same age groups are also in table E. Do the data show that the death from cardiovascular disease are in the same proportion as all deaths for the different age groups? Test at the 10% level. Hint: start by calculating the total cardiovascular frequency.
Table E: Deaths of Females for Different Age Groups
|
Age |
5-14 |
15-29 |
30-49 |
50-69 |
Total |
|
Cardiovascular Frequency |
10 |
27 |
60 |
480 |
|
|
All Cause Proportion |
0.14 |
0.16 |
0.22 |
0.48 |
|
Answer
State the hypotheses:
This is the null hypothesis Ho: Deaths from cardiovascular disease in females are in the same proportion as all deaths for the different age groups
The alternate hypothesis Ha: Deaths from cardiovascular disease in females are not in the same proportion as all deaths for the different age groups
We are already given alpha value of 10% in problem statement
The expected frequencies should not be less than 5 for obtaining a valid test statistic in Chi-square test. However, as will be seen below in table, none of these frequencies is less than 5.
The Chi-square statistic is calculated using the formula
Where O and E are the observed and the expected frequency values respectively. This can be tabulated as;
|
Age |
May-14 |
15-29 |
30-49 |
50-69 |
Total |
|
Cardiovascular Frequency |
10 |
27 |
60 |
480 |
577 |
|
Expected |
10.12246 |
27.11301 |
60.11581 |
479.6487 |
577 |
|
|
0.001481 |
0.000471 |
0.000223 |
0.000257 |
0.002433 |
|
All Cause Proportion |
0.14 |
0.16 |
0.22 |
0.48 |
1 |
|
Expected |
0.017543 |
0.04699 |
0.104187 |
0.83128 |
1 |
|
|
0.854782 |
0.271791 |
0.128737 |
0.148443 |
1.403753 |
|
Total |
10.14 |
27.16 |
60.22 |
480.48 |
578 |
|
Expected |
10.14 |
27.16 |
60.22 |
480.48 |
578 |
|
|
0.856263 |
0.272262 |
0.12896 |
0.1487 |
1.406186 |
The chi-square value is 1.406186
The degrees of freedom for the test are 3, since there are 4 values in table. The p-value, is 0.7041
Since the p-value is greater than the alpha level, we fail to reject the null hypothesis.
The result is not statistically significant at 0.1 level of significance. There is no sufficient evidence to support the claim that deaths from cardiovascular disease in females are not in the same proportion as all deaths of females for the different age groups.
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