130 SAMPLING FROM BINOMIAL POPULATIONS Ch. 5 



cent, or more, of the cartons probably contain too many mold particles? Use 

 a 99 per cent confidence interval as the basis for your answer. Arts. 21. 



9. Suppose that 100 cattle selected at random from a very large group have 

 been tested for tuberculosis. If 15 were found to be reactors, place an upper 

 limit on the proportion of reactors in the whole group if 95 per cent confidence 

 in the answer is considered adequate in these circumstances. 



10. The United States Department of Agriculture publication, Agricultural 

 Statistics, 1946, indicates that among United States herds of cattle which are 

 infected with Bang's disease at all, an average of 12 per cent of the cows have 

 the disease. Suppose that a large herd which has some incidence of the dis- 

 ease is to be tested by taking a random sample of 50 cattle. How many out 

 of the 50 must be free of the disease before the owner can be assured (at the 

 99 per cent level of confidence) that his herd is above average in freedom 

 from Bang's disease? Ans. 46. 



11. Calculate directly from the binomial series (q-\- p) i the 75 per cent con- 

 fidence interval on p if 3 out of 4 items sampled are found to be acceptable in 

 the sense employed earlier. Obtain the answer to the nearest whole per cent. 



12. Verify the entry in Table 5.21« for r = 5. 



13. Suppose that an entomologist wishes to know what percentage of the 

 corn plants in a large field have been infested to some degree by the southwest 

 corn borer. He thinks that the percentage is somewhere between 20 and SO, 

 but he wants to reduce that uncertainty to an interval of not over 15 percent- 

 age points. If he is willing to accept a risk of 5 in 100 of drawing an erroneous 

 conclusion, how large a sample must he take? 



14. Suppose that you are helping to administer a farm management associa- 

 tion and wish to learn what percentage of the members use a certain procedure 

 recommended for poultrymen. Suppose, also, that a random sample of 250 

 interviews reveals that 200 in the sample do use the recommended practices. 

 What can you say about the true percentage using this practice in the whole 



association? Ans. CI 95 : 74-85% 1 



2-86% J 



CI • 72- Ql - |USe P ractlces - 



5.3 TESTING PREDETERMINED HYPOTHESES 

 REGARDING p 



In some fields of investigation the probable magnitude of p can 

 be deduced from what appear to be reasonable theoretical considera- 

 tions, as was illustrated in the discussions of the A-B, and other, 

 blood groups. As another illustration, the theory of sex inheritance 

 might lead geneticists to conclude that male and female offspring of 

 human beings should be produced in equal proportions. If so, p = 1/2 

 when children are classified merely as male or female. Abundant 

 statistical evidence now exists to show that more than one-half the 

 children born in the United States are male; therefore, the original 

 hypothesis that p = 1/2 is known to be false. However, mankind 

 cannot afford to wait many years until the collection of a great 



