184 SAMPLING NORMAL POPULATIONS Ch. 6 



and hence the 95 per cent confidence interval is 



3.76 < n < 7.54, 

 which is very much like that derived from the ^-distribution. 



PROBLEMS 



1. Solve problem 1, section 6.4, with the G-test instead of the i-test. 



2. Solve problem 3, section 6.5, by means of the G-test. 



Aiis. G = 0.289; P^L .064; accept H n tentatively. 



3. Draw 25 samples, each with n = 10 from a near-normal population, and 

 compute the G for each sample. How many of these G's fall beyond 0.186 in 

 numerical size? How do your results check with Table IX? 



4. Suppose that a college is attempting to learn if instruction of a certain 

 type improved in one year a student's ability to think analytically. Also as- 

 sume that tests exist which reliably measure such ability, and that these tests 

 are given at the beginning and at the end of the school year. If the following 

 dijjereiices between the last and the first score of each student were obtained, 

 would the G-test cause you to accept or to reject the hypothesis that the teach- 

 ing procedures employed jailed to improve analytical thinking? 



X: 5, 0, 10, -4, -6, 8, 1, 7, -10, 0, 3, 5, -1, 8, 4, 0, -3, 7, 7, and 9. 



Am. G = 0.125; P = .05; reject H (fi = 0). 



5. Make up, and solve, a problem like problem 4, which has the same x but for 

 which G is twice as large. Half as large. 



6. Suppose that information is sought analogous to that in problem 4, but 

 there are two separate classes of 15 students being taught by each method. The 

 two classes are supposed to be equal at the start of the teaching period. Given 

 the following gains ( + ) or losses ( — ) in score during the year, draw appro- 

 priate conclusions by means of the G-test and Table X: 



Method I: 10, 3, -2, 5, 0, -8, 14, 1, -12, 5, 5, 9, 7, -1, and 9. 

 Method II: -2, 5, 5, 4, 0, 7, 6, -1, 4, 10, 8, 11, 10, 0, and 13. 



Ans. G = 0.114; P> .10; accept ff (/tj = p 2 ). 



7. An experiment intended to discover if blue fluorescent lights will increase 

 the vitamin C concentration in tomatoes on the seventh and eighth clusters 

 from the bottom of the plant gave these results, in milligrams per 100 grams: 



No extra light: 38.57, 39.39, 33.44, 34.32, and 38.01. 

 Blue fluorescent: 33.72, 37.85, 39.07, 31.16, and 35.69. 



Test the hypothesis that the blue light does not change the vitamin C con- 

 centration, and draw valid conclusions. 



8. Suppose that two methods of computing basal metabolism for the same 

 11 subjects produced the following pairs of records, in calories per square meter 

 per hour. 



31.42, 30.90, 34.92, 30.59, 30.53, 33.08, 32.61, 30.46, 

 30.73, 31.44, 32.82, 31.80, 29.16, 32.96, 32.32, 30.76, 

 30.55, 33.19, and 29.22. 2Xi = 347.47. 

 27.65, 32.54, and 29.30. 2A 2 = 341.48. 



