Question

Corn: In a random sample of 92 ears of corn, farmer Carl finds that 16 of...

Corn: In a random sample of 92 ears of corn, farmer Carl finds that 16 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 28% of Carl's corn has worms?

Yes, because 0.28 is below the upper limit of the confidence interval.No, because 0.28 is above the upper limit of the confidence interval.     No, because 0.28 is below the upper limit of the confidence interval.Yes, because 0.28 is above the upper limit of the confidence interval.

Homework Answers

Answer #1

a)

Point estimate of proportion = = 16 / 92 = 0.174

b)

Z critical value at 0.05 significance level = 1.96 (From Z table)

c)

Margin of error E = Z/2 * sqrt [ ( 1 - ) / n ]

= 1.96 * Sqrt [ 0.174 ( 1 - 0.174) / 92 ]

= 0.077

d)

95% confidence interval for p is

- E < p < + E

0.174 - 0.077 < p < 0.174 + 0.077

0.097 < p < 0.251

e)

We are 95% confident that less than 28% of Carl's corn has worms.

Yes, because 0.28 is above the upper limit of the confidence interval.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Corn: In a random sample of 92 ears of corn, farmer Carl finds that 14 of...
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...
Corn: In a random sample of 92 ears of corn, farmer Carl finds that 14 of...
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...
Corn: USE SOFTWARE In a random sample of 88 ears of corn, farmer Carl finds that...
Corn: USE SOFTWARE In a random sample of 88 ears of corn, farmer Carl finds that 15 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...
Corn: In a random sample of 92 ears of corn, farmer Carl finds that 16 of...
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...
Corn: In a random sample of 88 ears of corn, farmer Carl finds that 15 of...
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 zα/2) for a 99% confidence interval? Use the value from the...
Corn: In a random sample of 84 ears of corn, farmer Carl finds that 7 of...
Corn: In a random sample of 84 ears of corn, farmer Carl finds that 7 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) What is the critical value of z (denoted zα/2) for a 90% confidence interval? Use the value...
Corn: In a random sample of 88 ears of corn, farmer Carl finds that 14 of...
Corn: In a random sample of 88 ears of corn, farmer Carl finds that 14 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 zα/2) for a 99% confidence interval? Use the value...
In a random sample of 88 ears of corn, farmer Carl finds that 14 of them...
In a random sample of 88 ears of corn, farmer Carl finds that 14 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...
Corn: In a random sample of 80 ears of corn, farmer Carl finds that 7 of...
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...
Pinworm: In a random sample of 780 adults in the U.S.A., it was found that 76...
Pinworm: In a random sample of 780 adults in the U.S.A., it was found that 76 of those had a pinworm infestation. You want to find the 95% confidence interval for the proportion of all U.S. adults with pinworm. (a) What is the point estimate for the proportion of all U.S. adults with pinworm? 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...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT