Ch. 7 REVIEW PROBLEMS 239 



55. Suppose that two varieties of corn have been grown at the same experi- 

 mental farm during the same year, and that the following plot yields, in pounds, 

 have been obtained: 



No. 1: 12.1 12.8 15.2 14.0 13.5 13.6 14.3 12.9 13.9 and 14.7 

 No. 2: 14.6 12.9 15.6 14.3 14.8 13.4 13.8 15.3 16.0 and 14.5 



These field weights have been corrected for moisture content so that the variety 

 yields per acre can be compared directly with these data. Use the G-test to 

 test the hypothesis H (/j. 1 = n 2 ), where the /x's are the true means of the 

 varieties. 



56. The following data simulate those which might be obtained from an 

 experimental comparison of the effectiveness of two fertilizers on the yield of 

 orange trees in pounds per tree: 



Nitrogen (N): 74 89 90 72 78 76 84 79 81 76 and 80 

 N + Potash: 103 102 97 80 87 92 91 78 83 89 and 92 



The two groups of trees (one for N and the other for N-f P) were assumed 

 with good reason to be on equivalent areas of land before the two fertilizers 

 were applied. Test the hypothesis that the addition of potash does not affect 

 yield. .4ns. G = 0.488, n = 11, P ^.002; reject hypothesis. 



57. Referring to problem 56, use the G-test to place a 92 per cent confidence 

 interval on the true difference in average yield produced by adding potash 

 under these circumstances, and draw appropriate conclusions. 



58. The following numbers are the pounds of tobacco per acre yielded, on the 

 average, in the United States during the years indicated. Make a scatter 

 diagram and decide if the trend toward increasing yield can be reasonably 

 considered as linear if this is taken to be a sample. 



59. Referring to problem 58, again assume that this is a sample from a 

 bivariate population and compute, and interpret, the CI 90 on /3, the true slope 

 of the regression line. 



60. Solve as in problem 59, after substituting p, the true coefficient of linear 

 correlation, for /3. Ans. CI 90 : .86 ^ p ^ .98. 



61. The following data are the numbers of sugar-maple trees tapped each 

 year and the resulting pounds of sugar and sirup. If these data can be re- 

 garded as a sample, did the production per tree change during this period in 

 any orderly manner; and, if so, how? 



Year: 1929 1930 1931 1932 1933 1934 1935 



Trees 



(1000's): 12,951 13,158 12,092 12,064 12,009 12,099 12,341 

 Pounds 



(1000's): 3724 5856 3589 3748 3269 3488 4673 



