Question

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

Solution: H.:P5-14 = 0.10, P15-29 = 0.12, P30-49 = 0.26, P50-69 = 0.52 Hj: The proportions are not p5-14 = 0.10, P15-29 = 0.12, P30-49 = 0.26, P50-69 = 0.52 If the null hypothesis is true, expected frequencies can be calculated as below: Observed Expected Frequency Age Frequency fe fo-fe (f.-fe)? (f. -fe)?/fe 8 1874.890 36.548 5-14 15-29 -43.3 -45.56 16 513 x 0.10 = 51.3 513 x 0.12 = 61.56 513 x 0.26 = 133.38 513 x 0.52 = 266.76 56 30-49 50-69 -77.38 166.24 2075.714 5987.664 27635.738 433 33.719 44.892 103.598 Ef.-fe)?/fe = 218.756 If. = 513 Efe = 513 Test Statistic: 72 - 5 (fo - fe)" = 218.756 1 2 fe Degrees of Freedom = df = (number of categories - 1) Hence, df = (4 – 1) = 3 Critical value: Level of significance = a = 0.05 From the xa distribution table; the critical value of x2, having area in the upper tail to its right equal to 0.05 and for (df = 3), is given by: xô.05 = 7.815 Hence, critical value = 7.815 Rejection region = (7.815,)

Since the value of test statistic x2 = 218.756 falls in the rejection region, we reject the null hypothesis. Conclusion: Reject Ho; we can conclude that the proportions are not ps-14 = 0.10, P15-29 = 0.12, P30-49 = 0.26, P50-69 = 0.52