190 SAMPLING NORMAL POPULATIONS Ch. 6 



REVIEW PROBLEMS 



1. Who was Student, and how was his work connected with the development of 

 present-day methods of statistical analysis? 



2. Calculate the arithmetic mean and the standard deviation for a set of num- 

 bers, Y{, given that 2F = 900 grams, and 2F 2 = 55,465 grams 2 , where the Y's 

 are the weights of female rats at 28 days of age. There are 20 rats in the sample. 



Ans. y = 45 grams, s = 28.1 grams. 



3. Compute the 80 per cent confidence interval for problem 2 on the true 

 mean 28-day weight of such rats, and draw appropriate conclusions. 



4. What would be the general change in the confidence interval of problem 3 

 if 95 per cent limits instead of 80 per cent limits had been computed? What 

 would be the effect if the 2 1' 2 had been smaller, the remainder of the numbers 

 staying the same? 



5. Graph the binomial frequency distribution of the numbers of sums of 6 

 thrown with two unbiased dice on sets of 8 throws. 



6. Compute for problem 5 the probability that on any particular future set 

 of 8 throws at least 3 sums of 6 will be thrown. Ans. .087. 



7. Take any newspaper which lists prices of bonds and determine the median 

 price and also the range. 



8. Calculate the coefficient of variation for problem 2, using y in place of n and 

 s in place of <r, and tell what sort of information it provides about the weights of 

 the rats in the sample. Ans. C V = 62.4 per cent. 



9. Draw 10 samples of 12 members each from the laboratory population and 

 compute t and G for each sample, using the correct hypotheses regarding [*. 



10. Determine the upper limits of the 20th and 85th percentiles for the fre- 

 quency distribution of Table 6.31 and state what information they give. 



Ans. Upper limit of 20th percentile = 0.90 by interpolation, = 0.86 by Figure 

 6.31. Upper limit of 85th percentile = 1.12 by interpolation, = 1.10 by 

 Figure 6.31. 



11. If 100 t t were to be drawn at random from among those summarized in 

 Table 6.31, what is the expected number of them falling between t = and 

 t = 1.50? 



12. Following are some experimental results from tests of the breaking 

 strengths of the wet warp of rayon and wool fabrics in pounds: 



Rayon: 29.5, 31.0, 28.7, 29.1, 28.4, 28.9, 30.9, and 29.0. 

 Wool: 25.3, 28.9, 19.2, 25.1, 21.1, 31.4, 25.6, and 19.0. 



Does the difference in average breaking strength lie beyond the bounds of 

 reasonable sampling variation according to the i-test? Solve problem also by 

 the G-test, and compare the conclusions. ^X R = 235.5, 2X 2 R = 6939.33. 

 -LX W = 195.6, SX2 ir = 4921.48. 

 Ans. t = 3.10, 14 D/F, P = .008; reject H {ii t =» 2 ). G = 0.665, n = 8, P = 

 .002; reject H (n 1 = fi 2 ). 



13. Suppose that twelve 2 inch x 12 inch x 8 inch wood blocks were tested 

 for strength with the following results in thousands of pounds: 6.5, 17.0, 

 10.0, 15.1, 13.5, 16.4, 19.8, 7.7, 11.5, 14.5, 12.7, and 12.9. Place 95 per cent confi- 

 dence limits on the true average strength of such blocks, and interpret these 

 limits. 



