Answer to Question #103791 in Quantitative Methods for naomi kuria

Question

bureau of labor statistics want to use statistics to determine whether there is a difference between 2 countries on some measure of labor or between time periods of one country.hourly compensation in US dollars for manufacturing production workers in country A in 2015 and 2019 were $25.96 and $28.29 respectively.Hourly compensation for country B were $19.26 in 1995 and $23.89 in 2004.actual hours worked in country A in 2015 were 36.1and 35.5 in 2019.country B 37.1 in2015 and 35.9 in 2019. was the hourly labor cost higher in country A in 2019 than country B in 2019?

Answer 1

Plot the hourly compensation of A and the hourly compensation of B on the same graph (blue for B and orange for A) in Excel. Assume that the tendency is linear, that is, each year the compensation increases at a constant rate. Compare the results:

As we see, in 2019 the hourly compensation must be higher in country B, no matter what is the actual number of hours worked in both countries because we compare hourly values. The amount of actual hours worked in countries is excessive information for the estimation of the hourly labor cost.

The linear equations passing two points with coordinates $(x_1, x_2), (y_1, y_2)$ that describes the growth of hourly compensation were computed as follows:

$$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}.$$

For instance, substitute our values for country A:

$x_1=2015,\\ y_1=25.96;\\x_2=2019,\\y_2=28.29.$

$$\frac{x-2015}{2019-2015}=\frac{y-25.96}{28.29-25.96},\\ \space\\ \frac{x-2015}{4}=\frac{y-25.96}{2.33},\\$$

multiply both sides by $4\cdot2.33$:

$$2.33(x-2015)=4(y-25.96),\\ 2.33x-4694.95=4y-103.84,$$

express y:

$$y=\frac{2.33x-4694.95+103.84}{4}=0.5825x-1147.8.$$

The equation for B can be calculated likewise.