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47O Part V . From the Dats at Hand to the World at Larqe

4. :: The seller of a loaded die claims that it n'ill favorthe outcome 6. We don't believe that claim, and roll thedie 200 times to test an appropriate hvpothesis. OurP-vaiue turns out to be 0.03. \\rhich conclusion is appro-priate? Explain.a) There's a 37o chance that the die is tair.b) There's a 97'X, chance tl.rat ihe die is fair.c) There's a 3')1, chance ihat a loaded die could ran-

domly produce ihe results n-e obsen'ed, so it's rea-sonable to conclude that ihe die is fair.

d) There's a 3",' chance thai a fair die could randomlyproduce tlie resulis s'e observed, so it's reasonable toconclude ihat ihe die is loaded.

5. -\ compant''s old antacid formula provided relieffor 70 ,, of the people u'ho used it. The company tests anen- iormula to see if it is better, and gets a P-value of0.27. Is it reasonable to conclude that the new formulaand the oid one are equally effective? Explain.

6. ,- - . . A survey investigating whether the proportion oftoday's high school seniors who own their own cars ishigher than it was a decade ago finds a P-value of 0.017.Is it reasonable to conclude that more high schoolershave cars? Explain.

7. :' ': . . A friend of yours claims that when he tossesa coin he can control the outcome. You are skeptical andwant him to prove it. He tosses the coin, and you callheads; it's tails. You try again and lose again.a) Do two losses in a row convince you that he really

can control the toss? Explain.b) You try a third time, and again you lose. What's the

probability of losing three tosses in a row if the pro-cess is fair?

c) Would three losses in a row convince you that yourfriend cheats? Explain.

d) How many times in a row would you have to lose inorder to be pretty sure that this friend really can con-troi the toss? Justify your answer by calculating aprobability and explaining what it means.

8. --, . Someone hands you a box of a dozen chocolate-covered candies, telling you that half are vanilla creamsand the other half peanut butter. You pick candies at ran-dom and discover that the first three you eat are alivanilla.a) If there really n'ere 6 vanilla and 6 peanutbutter can-

dies in the box, what is the probability you wouldhave picked three vaniilas in a row?

b) Do you think there really might have been 6 of each?

neu, s),stem on 200 people, of whom 188 were successful.Is this strong evidence that the new system fails to meetthe company's goal? A student's test of this hypothesis isshorvn belort'. How many mistakes can you find?Ho t) - 9.96

HNt) + 0.96

sRS,0.96(200) > 10

w: o.nn, sD(p) =

0.96 - 0.94z- O* :I.IBP:P(z>1.18):0.12There is strong evidence that the new system does notwork.

10. :,:, r . ':. In November 2001, the Ag Globe Trotternewsletter reported that 90% of adults drink milk. A re-gional farmers' organization planning a new marketingcampaign across its multi-county area polls a randomsample of 750 adults living there. In this sample, 657people said that they drink milk. Do these responsesprovide strong evidence that the 90% figure is not accu-rate for this region? Correct the mistakes you find in astudent's attempt to test an appropriate hypothesis.Ho p - 0.9

Ha:p < 0.9

sRS,750 > 10

657,*: 0.876; SD(i) :_ 0.876 - 0.94 _ _.,z-

0.012P:P(z>-2):0.977There is more than a 97"1' chance that the stated percent-age is correct for this region.r rr,,, , . I r-:. In a rural area only about 30% of the wells thatare drilled find adequate water at a depth of 100 feet orless. A local man claims to be able to find water by "dows-ing"-using a forked stick to indicate where the wellshould be drilled. You check with 80 of his customers andfind that 27 have wells less than 100 feet deep. What doyou conclude about his claim? (We consider a P-value ofaround 57o to represent strong evidence.)a) Write appropriaie hypotheses.b) Check the necessary assumptions.c) Perform the mechanics of the test. What is the P-value?d) Explain carefully what the P-value means in this

context.e) What's your conclusion?

'l .., ,. .;i ,,.:: ,. In the 1980s it was generally believedthat congenital abnormalities affected about 5% of thenation's children. Some people believe that the increasein the number of chemicals in the environment has led to

: 0.017

:0.012

tl.

Explain.c) Would you continue to believe it if the fourth one

you try is also I'anilla? Explain.9. , ' ' . ,. Many people have trouble program- 12.

ming their VCRs, so a company has developed what ithopes will be easier instructions. The goal is to have atleast 96"/" of customers succeed. The company tests the

(0.e4) (0.06)200

(0.88)(0.12)750