Question

The data below are yields for two different types of corn seed thatt were used on adjacent plots of land.

Type 1    Type 2       

2024                2018

1917              1916

2009               2013

2551               2474

2252                2137

1889                1929

2185                 2161

1556                 1492

Construct a 95% confidence interval for the mean difference between the yields from the two different types of seed. type 1-type 2

Answer 1

Solution - The data below are yeilds for two different types of corn seed that were used on adjacent plots. of land Assume that the data are normally distróbuted. Type 1 Cai) 2024 1912 2009 255) 2252 1889 2185 1556 Cai-57)2 520.0156 17128.2656 1511.2656 253,134.7656 41667.0156 25241.2656 18803.2656 241941.0156 Type 2 (yi) 2018 1916 2013 2474 2137 1929 2161 1492 Cyi-y)? 0.25 10302.25 20.25 208392.25 14280-25 2832.25 20592.25 276150.25 0 Sample mean (7) - { = 16383 = 2042.8750 © sample mean (T) - yi = 16140 - 2017.5 16 sample standard deviation (51) = {(0-5) 599996.875 8-1 I'S = 292.7692 @_sample Standard deviation (82) = [191-g12 12-1 532520 8-

Ise = 272. 1203 | To find 95% confidence interval for the mean difference, Here, c=95% 420.95, I-820.05, */2 = 0.025 The sample sizes (ni and n2) < 30 and population standard, deviations are untenown then we have to use t- table trian2-2, 4/2 = 28+8-2, 0.025 = 214,0.025 Eni+n2-2, 2/2 = 2.145 Thus confidence interiel i (en-g) – taitne-2, 412 | Se + S22 ni 2 Gy) + EATER 2-2,212 SiR ni Sz? na (3.3) dayanaziala hone). (1207.8150 - 2012:8) – C2-15) / 192927 Cenya (2047.8750 - 2012-5) + (2.145) / (292.2692)2 + (227.1203)2 (30.375 - (305-7184) 30.375 + ( 305.7184) 21803) - (-275.3434, 336.0934) Thus 95% confidence internal for the mean difference between the yeilds from the two different types of seed type 2 - type 2 ie (441-42) is, (-275.3434 , 336.0934)