Corn: In a random sample of 140 ears of corn, farmer Carl finds that 19 of them
ID: 3234131 • Letter: C
Question
Corn: In a random sample of 140 ears of corn, farmer Carl finds that 19 of them have worms. Carl claims that less than 20% of all his corn has worms. Test this claim at the 0.05significance 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) 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.
Explanation / Answer
The statistical software output for this problem is:
One sample proportion hypothesis test:
p : Proportion of successes
H0 : p = 0.2
HA : p < 0.2
Hypothesis test results:
Hence,
a) p = 0.136
b) Test statistic = -1.90
c) P - value = 0.0286
d) Reject Ho
e) The data supports the claim that less than 20% of Carl's corn has worms.
Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 19 140 0.13571429 0.03380617 -1.9015971 0.0286