Question

1. Age	Rate US (per 100,000)	Population    Michigan	Population    Ohio
   0-24	80	3,210,500	3,930,600
   54-64	420	5,270,200	6,250,000
   65+	4500	1,350,000	1,750,100
   Total		9,830,700	11,930,700

   What is the expected number of deaths in Michigan using US rate?

   What is the expected number of deaths in Ohio using US rates?

   If the actual number of deaths in Michigan is 96,100. What is the standardized mortality ration for Michigan?

   If the actual number of deaths in Michigan is 123,250. What is the standardized mortality ration for Ohio?

   Which state had the best mortality rate?

   Does Michigan have the higher or lower mortality rates relative to the united states?

Answer 1

1 Expected number of death in Michigan

The formula t calculate the expected number of death is

age specific mortality rate of the other population under study x the number of population of a standard group.And finally add all these numbers for each age group

The number of people in the age group 0- 24 is 3,210,500 and the US rate is 80.Expected death of this age group  is 3,210,500 x 80 = 256,840,000

The number of population in the age group of 54 - 64 is 5,270,200,and the US rate is 420.So the expected death of this age group  is 5,270,200 x 420 = 2,213,484,000

The number of population above the age of 65 is 1,350,000 and the rate is 4500,Expected death of this age group  is 1,350,000 x 4500 = 6,075,000,000

when we add the expected death of all these age group we get the expected death of Michigan

That is 256,840,000 + 2,213,484,000 + 6,075,000,000 = 8,545,324,000

2 Expected number of death in Ohio

The formula to calculate the expected number of death is

age specific mortality rate of the other population under study x the number of population of a standard group.And finally add all these numbers for each age group

The number of people in the age group 0- 24 is 3,930,600 and the US rate is 80.Expected death of this age group  is 3,930,600 x 80 = 314,448,000

The number of population in the age group of 54 - 64 is 6,250,000 and the US rate is 420.So the expected death of this age group  is 6,250,000 x 420 = 2,625,000,000

The number of population above the age of 65 is  1,750,100and the rate is 4500,Expected death of this age group  is 1,750,100 x 4500 = 7,875,450,000

when we add the expected death of all these age group we get the expected death of Ohio

That is 314,448,000 + 2,625,000,000 + 7,875,450,000 = 10,814,898,000

3.Standardized mortality rate of Michigan

The formula to calculate the standardized mortality rate is the total number of observed death devided by the total number of expected death x 100

Here the actual death is given as  96,100.

so SMR = (96100 / 8,545,324,000 ) X 100 = 0.0011

4.Standardized mortality rate of Ohio

The formula to calculate the standardized mortality rate is the total number of observed death devided by the total number of expected death x 100

Here the actual death is given as   123,250

so SMR = (123,250 / 10,814,898,000) X 100 = 0.0011

5. The mortality rate of Michigan

The formula to calculate the mortality rate is the number of death devided by the number of total population

Here the number of actual death is given as 96100

Total population of Michigan is 9,830,700,When we put this values in the formula it will become 96100 / 9830700 =0.0097

The mortality rate of Ohio

The actual number of death in Ohio is given as 123,250 and the total population is 11,930,700

The mortality rate is 123250 /11930700 = 0.0103

Michigan has the less mortality rate and is considered as better than the Ohio.

6. The death rate of US is 420 + 80 +4500 = 5000

The number of population is given as 100,000

so the mortality rate is 5000 / 100,000 = 0.05

Michigan has the lower mortality rate than the US