2-proportions

2-proportions - B be the proportion of insect killed by...

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Hypothesis Test Example for Two Proportions (p 1 -p 2 ) Exercise 9.102 page 396 of Statistics , 7th Edition by McClave, Dietrich and Sincich: "A new insect spray, type A, is to be compared with a spray, type B, that is currently in use. Two rooms of equal size are sprayed with the same amount of spray, one room with A, the other with B. Two hundred insects are released into each room, and after 1 hour the numbers of dead insects are counted." There are 120 dead insects in the room sprayed with A and 90 in the room sprayed with B. Do the data provide enough evidence to indicate that spray A is more effective than spray B? Use α = .05. H a : Spray A is more effective than Spray B. (p A -p B >0 ) H o : Spray A is not more effective than Spray B. (p A -p B < 0) Assumptions: Two independent binomial experiments were performed. Let p A
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Unformatted text preview: B be the proportion of insect killed by Spray B. Since n A = n B = 200 with p ^ A = .6 and p ^ B = .45, the sampling distribution of p ^ A- p ^ B is approximately normal. Test Statistic: = .05 RR : z > 1.645 Calculation: Decision: Reject the null hypothesis. Conclusion: There is enough evidence to indicate that Spray A is more effective than Spray B. The p-value = P(z > 3.04) = .5 - .4988 = .0012. If the null hypothesis is true and the two insect sprays are equally effective a difference as large as this one would occur by chance 12 times in every 1000. Hence, there is evidence to indicate that Spray A is more effective than Spray B. 90% confidence interval for p A- p B We are 90% confident that Spray A kills between 7% and 23% more insects than Spray B....
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This note was uploaded on 12/11/2011 for the course STA 3123 taught by Professor Staff during the Fall '08 term at FIU.

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