170 SAMPLING NORMAL POPULATIONS Ch. 6 



age additional yield produced by the new method? Suppose that the new 

 method costs $5 per acre more to use than the older method. What can you 

 say about the probable economic advantage obtained from the new method if 

 wheat is currently bringing $2.25 per bushel? 



Ans. CI 95 : 2.65 — \x^ 7.35 bushels. Gain ^96 cents per acre. 



7. Suppose that in problem 6, s had been 10 bushels per acre. Show how this 

 increase in sampling variability among the 21 plots changes the answers to the 

 questions asked in problem 6. 



8. Suppose that in problem 6, the sample had involved but 10 plots. Show 

 how this decrease in the size of the sample changes the answers to the questions 

 asked in problem 6. 



9. Suppose that chemical analysis shows that the mean per cent protein for 16 

 wheat samples is 14.28 and that the estimated standard deviation for the popula- 

 tion of x's being sampled is sj = 2.00. What conclusions can you draw from the 

 99 per cent confidence interval on the true mean m? 



10. If basal metabolisms determined for a random sample of 25 sixteen-year- 

 old Kansas girls produced x = 45.80 calories per square meter per hour, withes = 

 0.50, what are the 80 per cent confidence limits, and what information do they pro- 

 vide in setting up a standard for sixteen-year-old Kansas girls? 



Ans. Cist): 45.67 < jj. < 45.93 calories per square meter per hour. 



11. Suppose that during a recent period of strong prices twenty-five 450-pound 

 choice steer calves were purchased, October 15th, wintered on silage and one pound 

 of cottonseed meal per day, and then sold on April 15th as choice stocker steers. 

 If the average net income per animal was x = $25 with s = $10, place a 90 per 

 cent confidence interval on the true average net income per animal for the popu- 

 lation so sampled. A similar sampling of choice 600-pound yearling steers pro- 

 duced a 90 per cent confidence interval of $105 to $130 net income per steer. What 

 conclusions can you draw regarding the most profitable choice for a cattleman to 

 make between these two systems? 



6.4 A STATISTICAL TEST OF A HYPOTHESIS 



THAT A GIVEN SAMPLE CAME FROM A 



NORMAL POPULATION WITH A 



SPECIFIED MEAN 



The general problem of deciding whether or not a particular sample 

 came from a normal population whose mean, fx, is specified but 

 whose standard deviation can be estimated only by means of s has 

 received consideration earlier in this chapter. In practice, the speci- 

 fication of fi is based upon a hypothesis about the population under 

 study. For example, if a new method of cultivating wheat does not 

 produce higher average yields the population of differences in yield 

 between the new and old methods grown in a series of paired plots 

 of land will have a true mean p. — because, on the average, there 

 is no advantage to the new method. If the hypothesis that ^ = 

 is found from statistical analysis to be unreasonable in view of the 



