Question

Corn: In a random sample of 92 ears of corn, farmer Carl finds that 16 of them have worms. He wants to find the 90% 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) Construct the 90% confidence interval for the proportion of all of Carl's corn that has worms. Round your answers to 3 decimal places.
< p <

(c) Based on your answer to part (d), are you 90% confident that less than 27% of Carl's corn has worms?

No, because 0.27 is below the upper limit of the confidence interval.No, because 0.27 is above the upper limit of the confidence interval.     Yes, because 0.27 is below the upper limit of the confidence interval.Yes, because 0.27 is above the upper limit of the confidence interval.

Answer 1

a)

Point estimate for proportion = 16 / 92 = 0.174

b)

90% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n ] < p < + Z/2 * sqrt [ ( 1 - ) / n ]

0.174 - 1.645 * sqrt [ 0.174 ( 1 - 0.174) / 92 ] < p < 0.174 + 1.645 * sqrt [ 0.174 ( 1 - 0.174) / 92 ]

0.109 < p < 0.239

c)

Yes, because 0.27 is above the upper limit of the confidence interval.