Chapter 4.5, Problem 21SLCT

To determine

To find the Florida mortality rate from adjusted data and compare it with mortality rate for the United States.

Explanation of Solution

Given:

	Age
	0-24	25-64	65 and older	Total
Florida deaths	3625	39820	129395	172840
Florida population	5716861	9842031	3375303	18934195
U.S. deaths	63208	619982	1832268	2515458
U.S. population	103542603	163960163	45296729	312799495
Total	109326297	174461996	50633695	334421988

Now, first need to calculate the U.S. population distribution for the age groups:

For age group 0-24:

U.S. population proportion for group 0-24:

  $\begin{array}{l}U.S.populationproportionforgroup0-24\\ =\frac{populationin0-24agegroup}{Populationsize}\\ =\frac{103542603}{312799495}\\ =33.10\%\end{array}$

Using above formula, we can find U.S. population proportion for age group 24-64

= 54.41%

U.S. population proportion for age group 64 and older

= 14.48%

Now, we can find the population distribution of Florida with respect to the population distribution for different age groups of U.S.:

For age group 0-24:

  $\begin{array}{l}\text{Florida }populationproportionforgroup0-24=U.S.populationproportionforgroup0-24\\ \frac{populationin0-24agegroup}{PopulationsizeofFlorida}\%=33.10\%\\ \frac{populationin0-24agegroup}{18934195}=0.3310\\ populationin0-24agegroup=6267580\end{array}$

Population for age group 24-64 for Florida: 9924740

Population for age group 64 and older for Florida:2741875

Now, we will compute the mortality rate for Florida with respect to the U.S. age group.

  $\begin{array}{l}Floridamortalityrateforage0-24\\ =\frac{Numberofdeathsin0-24agegroup}{OldpopulationofFloridain0-24agegroup}\times 1000\\ =\frac{3625}{5716861}\times 1000\\ =0.6\end{array}$

By using same formula, we can calculate,

Florida mortality rate for age 24-64=4.0

Florida mortality rate for age 64 and older=38.3

Now, we will calculate the number of deaths in Florida with respect to the new population distribution using the mortality rate.

  $\begin{array}{l}Floridamortalityrateforage0-24\\ =\frac{Newnumberofdeathsin0-24agegroup}{NewpopulationofFloridain0-24agegroup}\\ 0.6=\frac{Newnumberofdeathsin0-24agegroup}{6267580}\\ Newnumberofdeathsin0-24agegroup=2974\end{array}$

Using same formula,

New number of deaths in 24-64 age group=40155

New number of deaths in 64 and older age group=105112

Therefore, new calculated data is,

	Age
	0-24	25-64	65 and older	Total
Florida deaths	3974	40155	105112	149241
Florida population	6267580	9924740	18934195	35126515
U.S. deaths	63208	619982	1832268	2515458
U.S. population	103542603	163960163	45296729	312799495
Total	109877365	174545040	66168304	350590709

We know crude mortality rate from old data is,

Crude mortality rate of U.S. = 8

Crude mortality rate of Florida = 9.1

Therefore, using new data,

Crude mortality rate for U.S. = 8

Crude mortality rate for Florida = 7.9

Hence, new adjusted crude mortality rate of Florida us much closer to the Crude mortality rate for U.S. As there was difference in old data.