136 SAMPLING FROM BINOMIAL POPULATIONS Ch. 5 



10. Use a confidence interval approach to answer the question in problem 9, 

 and discuss the difference between the two methods. 



Ans. CI 95 : 30-50 per cent opposed. CI 99 : 27-54 per cent opposed. 

 Both include 48 per cent. 



11. Suppose that a poll of Topekans (Kansas) shows that one candidate re- 

 ceived 135 votes to 115 for the other candidate for a certain public office. Use 

 both the x 2 -test and confidence intervals to determine the probable winner, 

 if the election is to be held very soon so that no appreciable change in opinion 

 is expected. 



5.4 TESTING THE HYPOTHESIS THAT TWO RANDOM 



SAMPLES CAME FROM THE SAME BINOMIAL 



POPULATION 



The type of problem to which the tests described in this section 

 apply arises when two groups of observations have been taken under 

 somewhat different circumstances. The question to be answered is: 

 Did the difference in circumstances produce two distinct binomial 

 populations as far as can be told from these samples? For example, 

 consider a simulated test of two house-fly sprays, one made from 

 lethane the other from pyrethrum. Suppose that 500 house flies 

 have been placed in each of two wire cages, identical in all respects. 

 The lethane spray is applied to one cage, the pyrethrum spray to the 

 other, with the following results: 



Spray Dead Alive Sums 



Lethane 475 25 500 



Pyrethrum 450 50 500 



Totals 925 75 1000 



Actually, the lethane spray killed 95 per cent of the flies in its 

 cage, whereas the pyrethrum killed only 90 per cent. However, if 

 both cages had been sprayed with the same spray, different per- 

 centages would have been killed in the two cages in all probability. 

 How rarely would they have been as different as they were found 

 to be in this experiment? The x 2 -test introduced in section 5.3 can 

 be employed successfully in the solution of this problem. However, 

 there is no predetermined hypothesis regarding the magnitude of p 

 like that available before. Hence some other method must be used 

 to calculate the expected numbers needed in the x 2 -test. 



There is no theory regarding insecticides which will furnish an 

 expected proportion "dead" in the population; but it was observed 



