Sec. 5.2 POINT AND INTERVAL ESTIMATION OF p 129 



because even the upper limit of the 99 per cent confidence interval 

 on the true proportion of duds is below 5 per cent. 



The procedures demonstrated above are not suggested as sufficient 

 quality control measures in themselves, but they do illustrate prin- 

 ciples which are basic to acceptance sampling. 



PROBLEMS 



1. Suppose that 100 bolts have been taken at random from a large group 

 and that 2 have been found to be defective. What is the 99 per cent confidence 

 interval on the true proportion of defectives in the group sampled? 



2. Suppose that a sample of 250 Germans showed that 101 had type O blood. 

 Place 95 per cent limits (to nearest per cent) on the percentage of such Ger- 

 man persons having type O blood. Am. 34 to 46. 



3. The little fruit fly, Drosophila melanogaster, has been used so extensively 

 in genetic research that a great deal is known about the genes which it carries 

 on its chromosomes. Among these genes are some which produce what are 

 called recessive lethals because they kill the potential offspring at an early 

 stage of development if both chromosomes carry the gene for that particular 

 lethal. Mating studies are able to show if only one chromosome of a fly carries 

 a particular lethal-producing gene. Suppose that a sample of 250 flies is found 

 to include 10 which are carrying one particular lethal. What can you say about 

 the true proportion of lethal-carrying flies in this population? 



4. Suppose that two different strains of fruit flies have been developed in a 

 laboratory upon the basis of the numbers of eggs that the females laid per day. 

 Suppose also that a particular recessive lethal, l v has been discovered in both 

 strains; and that samples of 250 flies from each strain gave these results: strain 

 A had 18 lethals, strain B had 32 flies carrying lethals among the 250 examined. 

 What can you conclude about the true proportion of lethal-carrying flies in 

 each strain? Are these two proportions probably equal? 



5. Suppose that 50 apples have been selected at random from a tree which 

 has a very large number of apples. If 5 apples were found to suffer from a 

 certain blight, what percentage of blight do you estimate for the whole tree if 

 you wish to run a risk of onb' 1 in 20 that your answer is wrong as a result of 

 an anomalous sample? Do likewise for a risk of only 1 in 100 being in error. 



6. Suppose that 100 eggs are selected at random from a large shipment, and 

 that 5 are found to be stale. What would you set as the upper limit on the 

 percentage stale in the whole shipment if you can afford a risk of sampling 

 error of only 1 in 100? Ans. 13. 



7. If a sample of 250 gun barrels in a large shipment has been examined for 

 defects and none found to be defective, place 99 per cent confidence limits on 

 the true proportion of defective barrels in the whole shipment. Would a 

 sample of 250 be large enough if the shipment must contain one per cent, or less, 

 defective? 



8. If 250 one-pound cartons of butter are to be selected from a carload at 

 random and examined for mold particles, what is the maximum number which 

 can be found to contain too much mold before you should conclude that 5 per 



