Corn: In a random sample of 80 ears of corn, farmer Carl finds that 4 of them ha

Question

Corn: In a random sample of 80 ears of corn, farmer Carl finds that 4 of them have worms. Carl claims that less than 15% of all his corn has worms. Test this claim at the 0.01significance level.

(a) What is the sample proportion of corn with worms? Round your answer to 3 decimal places.

p =

(b) What is the test statistic? Round your answer to 2 decimal places.

(c) What is the P-value of the test statistic? Round your answer to 4 decimal places.
P-value =


(d) Choose the appropriate concluding statement.

The data supports the claim that less than 15% of Carl's corn has worms.There is not enough data to support the claim that less than 15% of Carl's corn has worms.     We reject the claim that less than 15% of Carl's corn has worms.We have proven that less than 15% of Carl's corn has worms.

Explanation / Answer

ans) a) the sample proportion of corn with worms p^ =X/n =4/80= 0.05

p = 15% = 0.15

standard deviation = sqrt(p(1-p)/n) =sqr((0.15*0.85)/80)=0.0399

b) tstat = p-p^/std/sqrtn

             =(0.05-0.15)/(0.0399/sqrt80) = 22.41

c) p value = 0.0056

d) There is not enough data to support the claim that less than 15% of Carl's corn has worms

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