You are designing a system to sort astringent mooseberries from delightful and n

Question

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)?

Mooseberries Red Seussberries Red Mooseberries Seussberries 596 289 blue blue 508 259 3557 3072 193 92 2864 2232 484 164 978 1094 325 105 2765 1434 212 267 2224 1169 157 305 1088 2711 314 88 1070 2647 367 164 1369 1106 271 86 2314 1654 246 75 1780 698 410 178 1135 826 326 68 2562 1491 541 225 1762 803 111 343 3207 1892 467 301 533 3228 318 71 2047 3282 294 97 1796 845 474 116 1339 888 427 136 3170 1208 334 190 2372 1360 459 256 2161 1855 499 315 2655 2748 528 331 3169 2924 506 137 3758 2897 522 126 3165 1494 518 134 3621 1275 459 196 3612 1346 253 299 2480 2094 270 282 1319 2583 143 204 1280 2225 199 339 709 2412 387 260 1136 3503 553 283 2067 2542 577 318 3058 2778 319 94 4007 3287 430 320 1521 866 520 213 1999 3470 520 343 2760 2307 526 242 3360 4181 3248 2489

Explanation / Answer

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

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