Sec. 6.4 TEST OF HYPOTHESIS H (p = «,) 175 



3. Solve as in problem 2, using the following data from the sixth and eighth 

 clusters of 10 plants: 



X: 7.0, 13.3, 8.6, 6.4, 8.3, 9.9, 2.6, 9.1, 6.6, and 1.6. 



You are given that SX = 73.4 and 2Z 2 = 643.40. 



4. During the winter tomatoes often are shipped green and allowed to ripen 

 in the package. Aside from matters of flavor and appearance, it is of interest 

 to know what effect this practice has on the vitamin C concentration in the 

 fruit. Two tomatoes were picked from each of 18 plants and at the same 

 cluster on the plant. One was red-ripe, the other was green (no red or yellow 

 coloring). The red-ripe member of each pair was analyzed immediately for 

 vitamin C; the other was ripened at room temperatume out of the sun until 

 red-ripe before its vitamin content was determined. Then the differences in 

 vitamin C between members of pairs was determined with the following results: 



2X = 49.37 milligrams/ 100 grams, favoring vine-ripened tomatoes, and 

 2X2 _ 387.5911. 



Determine statistically if there probably is a loss in ascorbic acid which is due 

 to picking tomatoes green and letting them ripen on the way to market or on 

 the shelf. 



5. Suppose that a sociologist has conjectured that the average rent for two-room 

 furnished apartments in a certain section of a city is $90 per month. A sample 

 of 20 apartments had x = $82.50, with s = $8. Use the t-test to determine if the 

 hypothesis Ho (n = 90) is acceptable when sampling variance is taken into account. 



6. Suppose that a timber cruiser has judged that the average breast-high diam- 

 eter of a certain stand of timber is 2 feet. Is the timber cruiser's estimate reason- 

 able if 31 trees are selected at random with these results: x = 2.3 feet and s = 0.8 

 feet? 



7. Suppose that a store conducts a study of the comparative net profits from 

 roasting ears sold in cellophane packs as compared to the loose ears in the husks. 

 The experiment is conducted for the 26 business days of a month. At the end of 

 each day, the net profit per ear is figured for each way of selling the corn. The 

 average advantage of using the cellophane pack on these 26 daily comparisons was 

 2 cents, with a standard deviation s = 0.5 cent. When sampling variation is con- 

 sidered, was the average advantage of the cellophane pack enough to justify the 

 conclusion that it is really more profitable? 



8. If, in a certain investigation, x = 10.5 and s = 3, how large must n be to 

 cause the rejection of the hypothesis: Hq (/j. = 0) at the one per cent level? 



9. If in a sampling study to which the t-test is appropriate the n is 28 and s = 5, 

 how large must x be before the hypothesis Ho (n = 0) will be rejected at the 5 per 

 cent level? 



10. Suppose that 27 pairs of plants of a certain species have been selected for 

 close similarity and are planted in pairs as close together as is appropriate for 

 this species. One member of each pair has had some boron added to the fer- 

 tilizer; otherwise the plants are treated identically. If the 30 plants having 

 boron outgrew their partners by an average of 3.6 centimeters, with the standard 

 deviation of the difference being s — 1.2 centimeters, is this sufficient evidence 

 for the statement that the addition of the boron produces some additional 

 growth ? 



