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Corn: In a random sample of 120 ears of corn, farmer Carl finds that 18 of...

Corn: In a random sample of 120 ears of corn, farmer Carl finds that 18 of them have worms. Carl claims that less than 20% 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.

p̂ =

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

z =

(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?

reject H₀fail to reject H₀

(e) Choose the appropriate concluding statement.

The data supports the claim that less than 20% of Carl's corn has worms.There is not enough data to support the claim that less than 20% of Carl's corn has worms. We reject the claim that less than 20% of Carl's corn has worms.We have proven that less than 20% of Carl's corn has worms.

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Answer:

Given that:

In a random sample of 120 ears of corn, farmer Carl finds that 18 of them have worms. Carl claims that less than 20% 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?

This is left tailed test

b) What is the test statistic?

Test statistic

The test statistic = -1.3713

c) What is the P-value of the test statistic?

d) What is the conclusion regarding the null hypothesis?

Fail to reject

e) Choose the appropriate concluding statement.

There is not enough data to support the claim that less than 20% of car's corn has worms.

orchestra answered 1 year ago

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