A preliminary investigation reported that approximately 20% of locally grown pou

Question

A preliminary investigation reported that approximately 20% of locally grown poultry were infected with an intestinal parasite that, though not harmful to those consuming the poultry, decreased the usual weight growth rates in the birds. A diet supplement believed to be effective against this parasite was added to the birds' food. Twenty birds were examined after having the supplement for at least two weeks, and five birds were still found to be infested with the parasite. (a) If the diet supplement is ineffective, what is the probability of observing five or fewer birds infected with the intestinal parasite? (Round your answer to three decimal places.) (b) If in fact the diet supplement was effective and reduced the infection rate to 10%, what is the probability observing five or fewer infected birds? (Round your answer to three decimal places.)

Explanation / Answer

Answer to the question)

Claim: Infected Proportion P = 0.20 or 20%

Sample size n = 20

Number of infected birds = 5

Thus sample proportion p^ = 5/20 = 0.40

.

Part a)

Standard error SE = sqrt(0.2*0.8/20) = 0.0894

.

Formula of Z is

Z = (0.40 -0.20) / 0.0894 = 2.237 ~ 2.24

P(x < = 5) = P( z < 2.24) = 0.9884 ~ 0.988

.

Part b)

SE = sqrt(0.10*0.90/20) = 0.0671

Z = (0.20-0.10) / 0.0671 = 1.49

P(x < 5) = P(z <1.49) = 0.932

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