Question

**Corn:** In a random sample of 88 ears of corn,
farmer Carl finds that 15 of them have worms. He wants to find the
99%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
*z*_{α/2}) for a 99% confidence interval?
**Use the value from the table or, if using software, round
to 2 decimal places.**

*z*_{α/2} =

(c) What is the margin of error (*E*) for a 99% confidence
interval? **Round your answer to 3 decimal
places.**

*E* =

(d) Construct the 99% 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 99% confident that
less than 30% of Carl's corn has worms?

No, because 0.30 is above the upper limit of the confidence interval.

No, because 0.30 is below the upper limit of the confidence interval.

Yes, because 0.30 is below the upper limit of the confidence interval.

Yes, because 0.30 is above the upper limit of the confidence interval.

Answer #1

a)

the point estimate for the proportion of all of Carl's corn that
has worms = 15/88 = **0.170**

b)

What is the critical value of *z* (denoted
*z*_{α/2}) for a 99% confidence
interval

Here then

c)

Margin of error is

M.E = **0.103**

**d)**

e)

**No, because 0.30 is above the upper limit of the
confidence interval.**

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