Question

Below are the data on work place fatalities per one million workers. 

Calculate the annualized rate of decline of worker fatality rates from 1875 to 2017. Also calculate the annualized rate of decline of worker fatality rates from 1875 to 1900, 1875 to 1912, 1875 to 1946, 1946 to 2017. Recall that the Men Who Built America basically covers 1875 to 1912 or 1926, compare and contrast the decline in workplace mortality during the Men Who Built America time period (1875-1912, 1875-1926) with the post World War II period, 1946 to 2017.

Answer 1

Annualized Worker Fatality Rate: It is the averaging rate of fatality on a annual basis.

Annualized Worker Fatality Rate = [ (Ending number of fatality/Beginning number of fatality)^1/n]-1

Here,

n= number of years

Annualized rate of decline of decline of worker fatality rate from from 1875 to 2017:

Annualized Worker Fatality Rate = [ (Ending number of fatality/Beginning number of fatality)^1/n]-1

Here,,

n= number of years

Ending number of fatality = 34

Beginning number of fatality = 2012

Number of year = 142 years

Annualized Worker Fatality Rate = [(34/2012)^1/142] - 1

= [(34/2012)^0.00704225] - 1

= [(0.0168986)^0.00704225] -1  

= 0.9716 -1 = -0.02832

-0.02832*100 = -2.83%

Annualized rate of decline of decline of worker fatality rate from from 1875 to 2017 = 2.83%

Annualized rate of decline of decline of worker fatality rate from from 1875 to 1900:

Ending number of fatality = 1001

Beginning number of fatality = 2012

Number of year = 25 years

Annualized Worker Fatality Rate = [(1001/2012)^1/25] - 1

=  [(1001/2012)^0.04] - 1

=  [(0.497514)^0.04] - 1

= 0.97246 - 1 = - 0.02753*100 = -2.75%

Annualized rate of decline of decline of worker fatality rate from from 1875 to 1900= 2.75%

Annualized rate of decline of decline of worker fatality rate from from 1875 to 1912:

Ending number of fatality = 544

Beginning number of fatality = 2012

Number of year = 37 years

Annualized Worker Fatality Rate = [(544/2012)^1/37] - 1

= [(544/2012)^0.02702] - 1

=  [(0.27037)^0.02702] - 1

= 0.0347*100 = -3.47%

Annualized rate of decline of decline of worker fatality rate from from 1875 to 1912 = 3.47%

Annualized rate of decline of decline of worker fatality rate from from 1875 to 1946:

Ending number of fatality = 310

Beginning number of fatality = 2012

Number of year = 89 years

Annualized Worker Fatality Rate = [(310/2012)^1/89] - 1

= [(310/2012)^0.0112359] - 1

=  [(0.154075)^0.0112359] - 1

= 0.9792 - 1 = -0.02079

= 0.02079*100 = -2.079%

Annualized rate of decline of decline of worker fatality rate from from 1875 to 1946 = 2.079%

Annualized rate of decline of decline of worker fatality rate from from 1946 to 2017:

Ending number of fatality = 34

Beginning number of fatality = 310

Number of year = 71 years

Annualized Worker Fatality Rate = [(34/310)^1/71] - 1

= [(34/310)^0.014084] - 1

=  [(0.109677)^0.014084] - 1

= 0.9693 - 1 = -0.03064

= 0.03064*100 = -3.064%

Annualized rate of decline of decline of worker fatality rate from from 1946 to 2017 = 3.064%

Annualized rate of decline of decline of worker fatality rate from from 1875 to 1926:

Ending number of fatality = 425

Beginning number of fatality = 2012

Number of year = 51 years

Annualized Worker Fatality Rate = [(425/2012)^1/51] - 1

= [(425/2012)^0.01960] - 1

=  [(0.21123)^0.01960] - 1

= 0.9699 - 1 = -0.03000

= 0.03000*100 = -3%

Annualized rate of decline of decline of worker fatality rate from from 1875 to 1926 = 3%

If we look at the date then found that annualized rate of decline of decline of worker fatality rate from from 1875 to 1912 = 3.47%, annualized rate of decline of decline of worker fatality rate from from 1875 to 1926 = 3% and annualized rate of decline of decline of worker fatality rate from from 1946 to 2017 = 3.064%. The annualized rate of decline of decline of worker fatality rate from from 1875 to 1912 is more  than annualized rate of decline of decline of worker fatality rate from from 1946 to 2017 and annualized rate of decline of decline of worker fatality rate from from 1946 to 2017 is little more than annualized rate of decline of decline of worker fatality rate from from 1875 to 1926. But there was no big gap between data percentage.