You are designing a system to sort astringent mooseberries f

You are designing a system to sort astringent mooseberries from delightful and nutritious seussberries. The berries which are otherwise indistinguishable from their outward appearance, vary slightly in their shades of blue. You build a custom color sensor using the APDS-9960 IC and a diffuse white light source, and record red and blue color data from 40 mooseberries and seussberries dropped in random orientations past the detector system (data summarized below). Propose a quantitative indicator using only the red and(/or) blue color data to sort the berries correctly. The client wants to make sure that at least 99% of the mooseberries are rejected by the sorter, while fewer than 5% of the seussberries are rejected. For your indicator, determine what the classification threshold should be, and report the respective probability that mooseberries or seussberries will be rejected based on this threshold. Does your system meet the client’s needs (please insert additional computational analysis as necessary)?

Solution

TEST FOR MEAN(Mooseberries Red) Vs MEAN (Mooseberries blue)

N Mean StDev SE Mean
C1 40 389 135 21
C5 40 2275 951 150

Difference = mu (C1) - mu (C5)
Estimate for difference: -1886
5% CI for difference: (-1896, -1877)
T-Test of difference = 0 (vs not =): T-Value = -12.42 P-Value = 0.000 DF = 40

here we accet the H0

TEST FOR MEAN(Seussberries Red) Vs MEAN (Seussberries Red)

N Mean StDev SE Mean
C6 40 2073 928 147
C2 40 207.8 92.3 15

Difference = mu (C6) - mu (C2)
Estimate for difference: 1865
95% CI for difference: (1567, 2163)
T-Test of difference = 0 (vs not =): T-Value = 12.65 P-Value = 0.000 DF = 39