Sec. 5.4 TEST OF THE HYPOTHESIS H (pi = Pz) 139 



dents of rural areas favor candidate A more strongly than do the 

 urban residents because the observed results are very unlikely to 

 be a sampling accident. 



PROBLEMS 



1. Lerner and Taylor, University of California, published the following data 

 on chick mortality in the Journal of Agricultural Gcience, Volume 60: 



How would you rate these sires as regards low progeny mortality after taking 

 account of sampling variability? 



2. Compute x 2 f° r the following practice data and obtain from Table V the 

 probability that sampling variation alone would produce a x 2 at least this 

 large. Also explain how information of this sort is used to test a hypothesis 

 about a binomial population. 



Answered 



Yes No Sum 



3. Given the following x 2 ' s > each with one degree of freedom, classify each 

 as probably due to chance alone, or not, if an event which is as unlikely to 

 occur as 1 time in 20 is considered to be purely a chance occurrence: 3.9, 7.1, 

 0.95, 2.1, 15.2, 8.7, and 1.2. 



4. Within what approximate limits do the lower 75 per cent of all sampling 

 values of x 2 with one degree of freedom lie when the hypothesis being tested 

 is correct? Ans. to 1.31. 



5. For a population of x 2 ' s each with one degree of freedom, the mean = ix 

 = 1, and the standard deviation = a = V2. Approximately what proportion 

 of the population of x 2 with 1 D/F (see Table V) lies in each of the following 

 ranges: /j. ± 1<t, fi =fe 2a, and fi ± 3o-? How do these proportions compare with 

 the corresponding snes for a normal distribution, as shown in Table III? What 

 information does this set of comparisons give about the shape of the chi-square 

 frequency distribution curve when x 2 h as one degree of freedom? 



