Corn: In a random sample of 80 ears of corn, farmer Carl finds that 4 of them ha
ID: 3273388 • Letter: C
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