Answer to Question #103945 in Math for Joseph

Question

Bureau of labor statistics wants to use statistics to determine whether there is difference between two countries on some measure of labor or between time periods for one country. The bureau reports that hourly compensation rates in US dollars for manufacturing production workers in country ‘A’ in 2015 and 2019 were $25.96 and $28.29 respectively. Hourly compensation rates for country ‘B’ over same period of time were $19.26 in 1995 and $23.89 in 2004. According to the survey by labor department the hours actually worked by employees per week in country A in 2015 were 36.1 and were 35.5 in 2019. For country B the figures were 37.1 in 2015 and 35.9 in 2019.
How will you help the department statistically to find whether the hourly labor cost in country A in 2019 was significantly higher than the 2019 hourly labor cost in country B based on given figures? (8marks)

Answer 1

hourly compensation rate in country A in 2019 - $28.29

To estimate hourly compensation rate in country B in 2019 we use we use the following formula (similar to compound interest formula):

P'=P*(1+a)^n

where n is the difference in years between P' and P hourly compensation rates, a = const

23.89 = 19.26*(1+a)^9

a=0.024 (close to inflation level)

P(2019) = 19.26*(1.024)^24 = $34.03

Let assume workers should work 8 hours a day.

Weekly Payroll Labor Cost (A) = 28.29*40 = 1132

Weekly Payroll Labor Cost (B) = 34.03*40 = 1361

hourly labor cost (A) = 1132/35.5 = 31.9

hourly labor cost (B) = 1361/35.9 = 37.9

According to our elavuations hourly labor cost in country B in 2019 was higher than in country A.