Question

A simple random sample with N=52 provided a sample mean of 21.0 and a sample standard...

A simple random sample with N=52 provided a sample mean of 21.0 and a sample standard deviation of 4.4.

a. Develop a 90% confidence interval for the population mean (to 1 decimal).

(________, _________)

b. Develop a 95% confidence interval for the population mean (to 1 decimal).

(________, _________)

c. Develop a 99% confidence interval for the population mean (to 1 decimal).

(________, _________)

d. What happens to the margin of error and the confidence interval as the confidence level is increased?

Homework Answers

Answer #1

a)

90% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

21 - 1.675 * 4.4 / sqrt(52) < < 21 + 1.675 * 4.4 / sqrt(52)

20.0 < < 22.0

90% CI is ( 20.0 , 22.0)

b)

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

21 - 2.008 * 4.4 / sqrt(52) < < 21 + 2.008 * 4.4 / sqrt(52)

19.8 < < 22.2

95% CI is (19.8 , 22.2)

c)

99% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

21 - 2.676 * 4.4 / sqrt(52) < < 21 + 2.676 * 4.4 / sqrt(52)

19.4 < < 22.6

99% CI is ( 19.4 , 22.6)

d)

As confidence level increases, margin of error and the width of confidence interval both increases.

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
A simple random sample with n = 52 provided a sample mean of 28.5 and a...
A simple random sample with n = 52 provided a sample mean of 28.5 and a sample standard deviation of 4.4. (Round your answers to one decimal place.) (a) Develop a 90% confidence interval for the population mean. to (b) Develop a 95% confidence interval for the population mean. to (c) Develop a 99% confidence interval for the population mean. to (d) What happens to the margin of error and the confidence interval as the confidence level is increased? As...
A simple random sample with n=56 provided a sample mean of 23.5 and a sample standard...
A simple random sample with n=56 provided a sample mean of 23.5 and a sample standard deviation of 4.5. a. Develop a 90% confidence interval for the population mean (to 1 decimal). (_____, ______) b. Develop a 95% confidence interval for the population mean (to 1 decimal). (_____, ______) c. Develop a 99% confidence interval for the population mean (to 1 decimal). (_____, ______) d. What happens to the margin of error and the confidence interval as the confidence level...
A simple random sample with n=50 provided a sample mean of 22.5 and a sample standard...
A simple random sample with n=50 provided a sample mean of 22.5 and a sample standard deviation of 4.2 . a. Develop a 90% confidence interval for the population mean (to 1 decimal). ( , ) b. Develop a 95% confidence interval for the population mean (to 1 decimal). ( , ) c. Develop a 99% confidence interval for the population mean (to 1 decimal). ( , ) d. What happens to the margin of error and the confidence interval...
A simple random sample with n=50provided a sample mean of 23.5 and a sample standard deviation...
A simple random sample with n=50provided a sample mean of 23.5 and a sample standard deviation of 4.3 a. Develop a 90% confidence interval for the population mean (to 1 decimal).   ,   b. Develop a 95% confidence interval for the population mean (to 1 decimal).   ,   c. Develop a 99% confidence interval for the population mean (to 1 decimal).   ,   d. What happens to the margin of error and the confidence interval as the confidence level is increased?
A simple random sample with n=54 provided a sample mean of 24.0 and a sample standard...
A simple random sample with n=54 provided a sample mean of 24.0 and a sample standard deviation of 4.3. a. Develop a confidence interval for the population mean (to 1 decimal). , b. Develop a confidence interval for the population mean (to 1 decimal). , c. Develop a confidence interval for the population mean (to 1 decimal). , d. What happens to the margin of error and the confidence interval as the confidence level is increased? - Select your answer...
A simple random sample with n = 57 provided a sample mean of 22.5 and a...
A simple random sample with n = 57 provided a sample mean of 22.5 and a sample standard deviation of 4.4. (Round your answers to one decimal place.) (a) Develop a 90% confidence interval for the population mean.    to   (b) Develop a 95% confidence interval for the population mean.   to   (c) Develop a 99% confidence interval for the population mean.    to  
You may need to use the appropriate appendix table or technology to answer this question. A...
You may need to use the appropriate appendix table or technology to answer this question. A simple random sample with n = 59 provided a sample mean of 26.5 and a sample standard deviation of 4.4. (Round your answers to one decimal place.) (a) Develop a 90% confidence interval for the population mean. to (b) Develop a 95% confidence interval for the population mean. to (c) Develop a 99% confidence interval for the population mean. to (d) What happens to...
Example Problem: [Ch 8, Q14] A simple random sample with n=54 provided a sample mean of...
Example Problem: [Ch 8, Q14] A simple random sample with n=54 provided a sample mean of 22.5 and a sample standard deviation of 4.4. Develop a 90% confidence interval for the population mean using the relevant fact: i) for a tdistribution with 53 degrees of freedom, ?(? > 1.674) = 0.05; ii) for a tdistribution with 54 degrees of freedom, ?(? > 1.297) = 0.10.
1. Develop 90 %, 95 %, and 99% confidence intervals for population mean (µ) when sample...
1. Develop 90 %, 95 %, and 99% confidence intervals for population mean (µ) when sample mean is 10 with the sample size of 100. Population standard deviation is known to be 5. 2. Suppose that sample size changes to 144 and 225. Develop three confidence intervals again. What happens to the margin of error when sample size increases? 3. A simple random sample of 400 individuals provides 100 yes responses. Compute the 90%, 95%, and 99% confidence interval for...
A simple random sample of 100 items from a population with a population standard deviation of...
A simple random sample of 100 items from a population with a population standard deviation of 9 resulted in a sample mean of 42. 1. Determine a 90% confidence interval for the population mean. 2. Determine a 95% confidence interval for the population mean. 3. What happened to the width of the confidence interval as the level of confidence increased from 90% to 95%?