Answer to Question #105023 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.
ii. How will you help the department statistically to find whether the difference between the two countries’ average workweek is significant or not?(7marks)

Answer 1

Country A hourly fee in 2019 is $ 28.29

To estimate the hourly compensation rate in country B in 2019, you can apply the 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

1.24 = (1 + a) ^ 9

1.024 = 1 + a

a = 0.024 (close to inflation)

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

Suppose workers must work 8 hours a day.

Labor costs per week (A) = 28.29 * 40 = 1132, 8*5=40

Labor costs per week (B) = 34.03 * 40 = 1361, 8*5=40

hourly wage (A) = 1132 / 35.5 = 31.9

hourly wage (B) = 1361 / 35.9 = 37.9

According to our estimates, the hourly labor cost in country B in 2019 was higher than in country A.