Question

A polling company takes a nationwide survey asking people whether they favor stricter laws on the sale of cigarettes. They find that 45% agree, 35% disagree, and 20% are undecided. In a more local simple random sample of size 200, 110 say they favor stricter laws, 60 are opposed, and 30 have no opinion. You're interested in whether these results differ significantly from the national findings. Which of the following gives the set of expected values for the test for goodness-of-fit?

A.

8.373, 1.4286, 2.5

B.

90, 70, 40

C.

45, 35, 20

D.

110, 60, 30

E.

20, -10, -10

Answer 1

B) 90, 70, 40 We test this with chi-square goodness of fit test Null hypothesis: True proportions in all 3 categories is equal to their expected value Alternative hypothesis: Atleast one proportions is different from its expected value Ho P10.45, p20.35, p3 0.2 Ha Atleast one pi do not match the claimed value Expected # (0-E)2 Expected Observed (O) fraction (p) 0.45 0.35 0.2 110 60 30 - np 90 70 40 4.444444 1.428571 2.5 8.373016 Test statistic:2 8.373 Significance level 0.05 Degrees of freedom , df-k-1-2 X0.05 has area of 0.05 to its right. To find X205 , open any Chi-square table, go across from row df 2 and down from column 0.05 and get 5.991 Critical value: X 25.991 Decision Rule: Reject Ho if2 >5.991 We can also use excel to find exact value: CHISQ. INV.RT C0.05,2) - 5.99146454710798 To get p-value, we can use excel fucntion CHÍSQ.DIST . RT ( 8.373 016 , 2) 0.015 199 269~ 0.0152 Since test statistic is greater than critical value , we reject null hypothesis. At 5% level, there is significant evidence that atleast one of the proportions differs from its claimed value