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 z? Use the answer found in the z-table or round to 3 decimal places.
z_α =

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

reject H₀fail to reject H₀    

(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