Question

**Corn:** In a random sample of 80 ears of corn,
farmer Carl finds that 7 of them have worms. Carl claims that less
than 20% of all his corn has worms. Test this claim at the 0.01
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? **Use the
answer found in the z-table or round to 4 decimal
places.**

P-value =

(d) What is the critical value of

(e) What is the conclusion regarding the null hypothesis?

reject *H*_{0}fail to reject
*H*_{0}

(f) 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.

Answer #1

a)

pcap = 7/80 = 0.088

b)

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: p = 0.2

Alternative Hypothesis, Ha: p > 0.2

Test statistic,

z = (pcap - p)/sqrt(p*(1-p)/n)

z = (0.088 - 0.2)/sqrt(0.2*(1-0.2)/80)

z = -2.50

c)

P-value Approach

P-value = 0.0062

d)

Rejection Region

This is right tailed test, for α = 0.01

Critical value of z is -2.326.

e)

fail to reject H0

f)

The data supports the claim that less than 20% of Carl's corn
has worms

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