11.2.4
In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in table #11.2.6 ("Global health observatory," 2013). In addition, the proportion of deaths of females from all causes for the same age groups are also in table #11.2.6. 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 5% level.
Table #11.2.6: Deaths of Females for Different Age Groups
Age |
5-14 |
15-29 |
30-49 |
50-69 |
Total |
Cardiovascular Frequency |
8 |
16 |
56 |
433 |
513 |
All Cause Proportion |
0.10 |
0.12 |
0.26 |
0.52 |
Here we are to test
H0: the proportions are equal
against
H1:the proportions are different
The given data is presented as
Age | Observed frequency(fi) | Expected probability | Expected frequency(npi0) | (fi-npi0)/npi0 |
5-14 | 8 | 0.1 | 51.3 | -0.844054581 |
15-29 | 16 | 0.12 | 61.56 | -0.740090968 |
30-49 | 56 | 0.26 | 133.38 | -0.580146949 |
50-69 | 433 | 0.52 | 266.76 | 0.623181886 |
Total | 513 | 1 | 513 | -1.541110611 |
The test statistic is given by
The test statistic follows chi square distribution with df 3
The critical value is obtained as
As the observed value is less than the critical value, we fail to reject the null hypothesis at 5% level of significance and hence conclude that the 2 proportions are not statistically different.
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11.2.4 In Africa in 2011, the number of deaths of a female from cardiovascular disease for...
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