Corn: In a random sample of 92 ears of corn, farmer Carl finds
that 14 of them have worms. He wants to find the 95% confidence
interval for the proportion of all his corn that has worms.
(a) What is the point estimate for the proportion of all of
Carl's corn that has worms? Round your answer to 3 decimal
places.
(b) What is the critical value of z (denoted zα/2) for a 95%
confidence interval? Use the value from the table or, if using
software, round to 2 decimal places.
zα/2 =
(c) What is the margin of error (E) for a 95% confidence
interval? Round your answer to 3 decimal places.
E =
(d) Construct the 95% confidence interval for the proportion
of all of Carl's corn that has worms. Round your answers to 3
decimal places.
< p <
(e) Based on your answer to part (d), are you 95% confident
that less than 26% of Carl's corn has worms?
Yes, because 0.26 is below the upper limit of the confidence
interval.
No, because 0.26 is above the upper limit of the confidence
interval.
No, because 0.26 is below the upper limit of the confidence
interval.
Yes, because 0.26 is above the upper limit of the confidence
interval.