Corn: In a random sample of 80 ears of corn, farmer Carl finds that 5 of them ha

Question

Corn: In a random sample of 80 ears of corn, farmer Carl finds that 5 of them have worms. Carl claims that less than 15% of all his corn has worms. Test this claim at the 0.05 significance level. (a) What is the sample proportion of corn with worms? Round your answer to 3 decimal places. (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) What is the conclusion regarding the null hypothesis? o reject Ho O fail to reject Ho (e) Choose the appropriate concluding statement. O The data supports the claim that less than 15% of Carl's corn has worms. O There is not enough data to support the claim that less than 15% of Carl's corn has worms. o we reject the claim that less than 15% of Carl's corn has worms. o we have proven that less than 15% of Carl's corn has worms.

Explanation / Answer

SOLUTIONA:

Ho:p=15%=0.15

H1:p<0.15

p^=x/n=5/80=0.0625

p^=0.063(3 decmals)

SOLUTIONB:

Z=p^-p/sqrt(p(1-p)/n)

=0.063-0.15/sqrt(0.15(1-0.15)/80)

=-2.18

Z=-2.18

Solutionc:

For z=-2.18

alpha=0.05

p=0.0146

Solutiond:

since p<alpha

0.0146<0.05

Reject Ho

Solutione:

the data supports the claim that less tha 15% of caarl's corn has worm

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