Question

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

Answer 1

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

2 Xobserved (fi - np!) np! -1.541110611 i=1

The test statistic follows chi square distribution with df 3

The critical value is obtained as

$\chi^2_{0.05,3}=7.815$

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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