174 



SAMPLING NORMAL POPULATIONS 



Ch. 6 



of the magnitude of jjl, now that the hypothesis H Q {/i — 0) is rejected, 

 confidence intervals can be obtained at any appropriate level of 

 confidence. 



PROBLEMS 



1. Suppose that 20 pairs of college students have been so selected that the 

 members of each pair can be considered equal in intelligence, scholastic records, 

 and in other factors associated with the making of good scholastic records in 

 a college. Suppose one member of each pair is enrolled in a class in social 

 science which is to be taught by a discussion method emphasizing analysis of 

 problems and reflective thinking; whereas the other member of each pair is put 

 in a class taught by a more formal lecture-recitation procedure. The subject to 

 be studied is the same in each class, and the teachers are considered to be equal 

 in teaching abilities. At the end of the teaching period all 40 students are given 

 the same examination with the following results: 



The discussion method appears to be the better for producing good test 

 scores, but there is considerable variation. Test the hypothesis that the two 

 methods actually are equal on the average (that is, /i = 0) and draw appropriate 

 conclusions. 



2. A study was made to determine if tomatoes high up on a plant have more 

 ascorbic acid (vitamin C) than those lower down on the same staked plant. To 

 study this matter, 10 pairs of red-ripe tomatoes were taken from 10 plants, with 

 one member of each pair being from the fifth cluster and the other from the 

 seventh cluster from the bottom of each plant. Each of the tomatoes from the 

 seventh cluster had more vitamin C than the corresponding tomato from the 

 fifth cluster by the following respective amounts: 



X: 6.6, 11.6, 10.9, 7.4, 8.8, 10.3, 7.4, 7.8, 5.8, and 4.0 milligrams/100 grams. 



Given that JZX = 80.6 and SX 2 = 700.46, compute a 90 per cent confidence inter- 

 val on the true average amount by which the ascorbic acid in tomatoes at the 

 seventh cluster exceeds that at the fifth cluster on the same plant, and draw 

 appropriate conclusions regarding /i. 



Ans. CI 90 : 6.7^/* ^9.4 milligrams/100 grams. 



