The horseshoe crab width values in Table 4.3 have xÌ… = 26.3 and s_x= 2.1. If the true relationship were similar to the fitted equation in Section 5.1.3, about how large a sample yields P(type II error) = 0.10, with α = 0.05, for testing H₀: β = 0 against H_α: β > 0?

Table 4.3:

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Number of Crab Satellites by Female's Characteristies Wt Sa cs w Wt Sa C S W Wt Sa C s W Wt Sa 23 28.3 3.05 83 3 225 1.55 33 26.0 2.60 4 33 25.6 2.1503 3 243 2.15 42 21.0 L8S 2 3 29.0 3.00 1 4 3 24.7 2.20 0 2 3 274 2.70 5 2 2 23.2 1.95 1 2 25.0 2.30 3 2 1 225 1.60 13 3 26.7 2.60 2 4 3 258 200 43 26.2 1.300 2 3 28.7 3.15 23 249 2.10 0 1 1 29.3 3.20 21 25.7 2.00 8 2 1 26.7 2.70 2 3 27.5 3.15 6 4 3 234 1.90 11 26.1 2.80 511 27.7 2.50 33 28.9 280 42 3 282 2.60 2 1 30.3 3.60 3 4 3 24.7 2.10 2 3 229 1.60 4 21 25.7 2.00 52 3 28.3 3.00 15 2 3 27.2 2.70 33 26.2 2.30 3 21 278 2.75 33 24.5 2.0S 23 30.0 3.05 8 2 3 29.0 3.20 10 2 3 26.2 2.40 23 26.2 2.40 3 3 3 25.6 2.80 73 3 23.0 1.65 1 3 3 23.0 1.80 23 254 2.25 63 3 24.2 1.90 2 3 25.4 2.25 43 3 25.7 1.20 43 27.5 290 03 3 23.1 1.65 4 3 27.0 2.25 3 23 285 3.05 22 24.0 1.70 21 28.7 3.20 03 3 23.1 1.55 33 26.5 1.97 13 3 245 2.20 13 3 28.5 3.00 1 2 3 28.2 287 23 24.5 1,60 1 011 26.0 2.30 9 3 3 248 2.10 03 2 24.7 1.90 0 2 1 23.7 1.95 02 3 25.8 2.65 0 2 3 282 3.05 11 2 3 238 2.10 021 26.0 2.30 14 1 1 27.1 2.95 82 3 252 200 321 26.8 2.70 5 4 3 275 260 0 2 2 25.7 2.00 54 3 23.7 1.85 0 2 3 26s 265 02 3 27.9 2.80 6 3 3 275 3.10 6 21 30.0 3.30 5 3 285 3.25 62 3 25.0 2ho 4 2 3 285 3.00 4 13 25.8 2.60 3. 52 3 27.7 2.90 51 1 27.4 270 0 4 3 25.5 2.25 0 3 3 27.1 255 323 26.0 2.15 5 2 3 280 280 0 21 265 1.30 5 3 1 27.0 2.45 02 2 229 1.60 0 3 2 26.0 220 02 3 25.1 2.10 5 3 2 245 225 031 25.9 2.55 4 2 3 258 230 041 25.5 2.75 0 4 3 23.S 1.90 521 26.8 2.55 o 4 3 26.7 245 021 29.0 2.80 1 3 3 255 225 0 2 1 29.7 3.85 2 3 275 2.5S 2 3 263 2.40 4 21 25.2 2.00 12 3 253 1.90 6 3 3 25.7 2.10 12 2 24,7 2.55 12 3 29.0 3.10 323 27.0 2.50 33 27.3 2.90 23 26.5 2.30 4 23 278 3.25 2 3 25.0 2.10 2 2 3 31.9 3.33 2 4 3 23.7 1.80 0 4 3 293 3.23 12 33 22.0 140 0 2 3 250 2.40 11 30.2 3.28 2 2 254 2.30 2 1 249 2.30 61 2 245 1.95 6 2 3 25.1 1.80 0 2 1 280 290 43 258 2.25 10 33 27.2 2.405 2 3 30.5 3.32 3 3 3 290 2.92 4 3 25.0 2.10 8 2 1 31.7 3.73 423 29.5 3.02 4 3 3 24.0 1.90 10 2 3 30.0 3.00 9 2 3 27.6 2.85 2 1 22.9 1.60 2 3 23.9 185 2 3 26.0 2.28 3 23 258 2.2003 3 24.1 1.80 33 29.0 3.28 41 1 280 2.62 1 1 26.5 2.35 0 53 3 27.0 2.50 6 3 3 23s 1.80 02 3 24.2 1.65 2 2 3 27.4 290 34 3 22.5 1.47 6. 2 3 3 262 2.22 03 3 284 3.20 4 2 3 26.2 202 2 3 27.9 3.05 72 3 24.9 2.20 02 1 284 3.10 2 2 25.0 225 6 23 27.5 2.63 321 24.3 2.00 6 21 335 5.20 0 23 258 2.40 423 26.2 2.30 023 24.7 1.95 03 2 29.8 3.50 84 3 25.7 2.15 0 2 3 265 2.75 03 3 26.2 2.17 2 3 3 26.I 2.75 0 4 3 27.0 2.63 02 2 245 2.00 0 2 1 23.1 200 4 2 3 283 3.20 4 2 3 265 2.35 0 4 3 245 1.90 2 3 3 238 1.80 2 3 28.2 3.05 "C, color (1, light medium; 2, medium; 3, dark medium; 4, dark), S, spine condition (1, both good; 2, one worn or broken; 3, both worn or brokenk W, carapace width (cm)k Wt, weight (kgk Sa, number of satellites.