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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
x²	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
x²	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
x²	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.

statistics Stat-200 p-value chi-square null hypothesis alternate hypothesis

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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): Expert Solutions for Success

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