Sec. 7.3 STANDARD DEVIATION ABOUT TREND LINE 215 



The only change in the computations is that the standard deviation 

 of Y now is 



sy = s y . x Vl/n + x 2 /2(x?) = 0.679(0.251) = 0.170 pound 



instead of the 0.700 pound obtained for the individual. It follows 

 that the required confidence interval is: 



CI94: 13.5 pounds < n y . x < 14.5 pounds, 



to the nearest one-half pound. This is a narrower interval than is 

 obtained for problem 7.31, as should be expected. 



PROBLEMS 



1. Compute sy and s y . x for the data for Figures 7.11^4 and G and relate their 

 comparative sizes to the scatter diagrams. 



2. Work problem 1 for Figures 7.115 and G. Does the downward trend of the 

 points on a scatter diagram, as contrasted with an identical upward trend, have 

 anything to do with the comparison between sy and s y . x l 



Ans. B: s Y = 16.0, s y . x = 3.1; G: s Y = 9.2, s y . x = 9.8. 



3. Referring to Figure 7. HE and the associated data, compute and compare 

 sy and s y . x as in problem 1. Could you have predicted from the scatter diagram 

 that they would be of essentially the same magnitude? Why? 



4. By visual inspection of Figures 7.1 1C, D, and F what do you conclude about 

 the comparative sizes of sy and s y . x for each figure? 



5. For the two sets of data in problem 7, section 7.1, compute the percentage 

 reduction in the standard deviation of the F; achieved if variability is measured 

 about the linear trend line rather than about the line Y = y for each set. Discuss 

 the two results obtained for the two sets in terms of the curvilinear trend in one set. 



6. Use the data of problem 1, section 7.1, to estimate the average Y for X = 13. 

 Also compute the standard deviation of this estimate, first considering a group 

 with X = 13 and then for an individual with X — 13. 



Ans. Y = 345.7 when A' = 13; s Y = 0.53; 1.01. 



7. Use the data of set B, problem 7, section 7.1, to place 92 per cent confi- 

 dence limits on the log(weight) of the 7-day-old bee larvae of the kind repre- 

 sented by this sample. Interpret these limits. 



8. Compute the 99 per cent confidence interval on /3 for problem 1, section 

 7.1, and draw appropriate conclusions. Ans. CI 99 : 21.2 ^ /3 ±£ 23.0. 



9. The following data express the farm population (as defined for the 1950 

 census) as a percentage of the total U. S. population: 



These are not sampling data, but the fitting of a trend line to these data may 

 be useful anyway. For example, if the war years, 1943 to 1945, inclusive, are 



