Sec. 6.5 TEST OF HYPOTHESIS H (fn = M2) 181 



5. An experiment designed to find out if supplemental lighting with incan- 

 descent lights will increase the vitamin C content of greenhouse tomatoes pro- 

 duced the following results in milligrams per 100 grams for tomatoes on the 

 bottom two clusters of the plants: 



No extra light: 25.92, 28.08, 21.27, 22.53, 26.27, 22.57, 22.57, 30.19, and 20.35. 



SZ = 219.75, 2A 2 = 5454.8279. 

 Incandescent: 20.30, 29.21, 20.50, 21.50, 23.71, 29.34, 26.32, 15.55, and 29.56. 



2A = 215.98, 2A 2 = 5378.5612. 



Use the t-test to decide whether or not the incandescent lights changed the 

 average ascorbic acid concentration in the greenhouse tomatoes. 



6. Given the following two sets of simulated data, assume first that the obser- 

 vations are paired (vertically) and compute and interpret the t. Then assume 

 that the observations are not paired and again do a £-test. Compare these 

 results and the hypotheses tested. 



A: 85 72 28 59 75 46 39 68 53; 2A = 525. 2A 2 = 33,369. 



B: 80 65 24 58 65 40 38 60 42; 2 A = 472. SA 2 = 27,198. 



Am. (a) t = 4.97, 8 D/F, reject H (n = 0). 



(b) t = 0.78, 18 D/F, accept H (ha = m ). 



7. The antibiotic, aureomycin, has been found to be a growth stimulant for 

 certain animals. The discovery is illustrated by the following two sets of data 

 obtained at Kansas State College under the direction of Dr. E. E. Bartley of 

 the Department of Dairy Husbandry. The measurement of growth used is the 

 total gain during a 12-week period, expressed as a percentage of birth weight. 



Obtain the 95 per cent confidence interval on the true difference between the 



two means fi 1 and /* 2 and tell what information this interval makes available. 



8. Suppose that 31 rainbow trout and 31 brook trout are taken at random 



