A company produces and sells widgets. The production process involves using labor and capital as inputs. The company is interested in estimating the production function that relates the quantity of widgets produced (Y) to the amount of labor (L) and capital (K) used. The company collects data on the quantity of widgets produced, the amount of labor, and the amount of capital used for 20 production runs. The data are presented in the table below:

Production run	Y (widgets)	L (labor, hours)	K (capital, units)
1	100	10	5
2	140	12	6
3	190	14	7
4	250	16	8
5	320	18	9
...	...	...	...
20	820	40	20

(a) Calculate the sample mean and sample standard deviation of Y, L, and K.

(b) Plot a scatter plot of Y against L and K separately.

(c) Estimate the Cobb-Douglas production function of Y on L and K.

(d) Interpret the estimated coefficients of L and K.

(e) Calculate the elasticity of production with respect to labor and capital, and interpret the results.

(f) Test the hypothesis that the elasticity of production with respect to labor is equal to 0.5, and interpret the results.