Question

What is a confidence interval for a population mean? How does it change when you increase...

What is a confidence interval for a population mean? How does it change when you increase the sample size? How does it change when you raise the level of confidence? Are these corresponding changes to the confidence interval intuitive?

Homework Answers

Answer #1

A confidence interval for the mean is a way of estimating the true population mean. Instead of a single number for themean, a confidence interval gives you a lower estimate and an upper estimate.  

Formula for confidence interval is

Xbar +- z* (sigma/ √n)

Increasing sample size will decrease the width of the confidence interval .

When we raise the confidence level the width of the confidence interval increases and we confident that the true value will lie in the interval.

No, the are totally based on the formula but not intuitive . Logically if we see all of this makes sense . Because increasing the confidence level must increase the width so that we can be more confident and likewise its with the sample size.

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
The width of a confidence interval estimate for a population mean when the population standard deviation...
The width of a confidence interval estimate for a population mean when the population standard deviation is known will (A)   become narrower if the size of the sample being used is increased and the confidence level is unchanged. (B)    not change if only the sample size is increased. (C)    become wider if the sample size remains the same and the confidence level decreases. (D)   become narrower if the size of the sample is decreased and the confidence level is unchanged....
The length of a confidence interval changes when either the confidence level changes or the sample...
The length of a confidence interval changes when either the confidence level changes or the sample size changes. To illustrate this, imagine a statistician takes a sample from a population with a population standard deviation of 2. The sample mean is calculated to be 10. Construct 3 different confidence intervals: 3a) Assume the sample size is 30 and the confidence level is 95% 3b) Assume the sample size is 30 and the confidence level is 90% 3c) Assume the sample...
You intend to estimate a population mean with a confidence interval. You believe the population to...
You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 7. Find the critical value that corresponds to a confidence level of 85%.
When constructing a confidence interval estimate for a population mean​ (when the standard deviation of the...
When constructing a confidence interval estimate for a population mean​ (when the standard deviation of the population is​ known), what is the calculation that has to be made to obtain the error​ margin? A. You multiply the number of standard deviations by the standard deviation of the sampling distribution of sample means. B. You subtract the sample mean from the population mean and then divide by the standard deviation of the population. C. You divide the standard deviation of the...
Find the margin of error for a​ 95% confidence interval for estimating the population mean when...
Find the margin of error for a​ 95% confidence interval for estimating the population mean when the sample standard deviation equals 90 with a sample size of​ (i) 484 and​ (ii) 1600 ​(i) Find the margin of error for a​ 95% confidence interval for estimating the population mean when the sample standard deviation equals 90 with a sample size of 484 (ii). ​(ii) Find the margin of error for a​ 95% confidence interval for estimating the population mean when the...
Mean Sample standard deviation Population standard deviation Sample size Confidence level Confidence interval 100 20 na...
Mean Sample standard deviation Population standard deviation Sample size Confidence level Confidence interval 100 20 na 25 95 % 100 20 na 25 90 % 100 40 na 25 90 % 100 40 n.a. 16 90 % 100 n.a. 40 16 90 % How does the confidence level affect the width of the confidence interval, other things equal? How does the size of the standard deviation affect the width of the confidence interval, other things equal? How does sample size...
In estimating a population mean with a confidence interval based on a random sample X1,... ,Xn...
In estimating a population mean with a confidence interval based on a random sample X1,... ,Xn from a Normal distribution with an unknown mean and a known variance, how the length of the confidence interval changes if we decrease the sample size from 9n to n?
Suppose you are calculating the minimum sample size required for a confidence interval about a population...
Suppose you are calculating the minimum sample size required for a confidence interval about a population mean and you know σ. Which of the following does not influence the minimum sample size? A. the size of the population B. confidence level C. the acceptable margin of error D. the size of the population standard deviation (σ)
Find the margin of error for a​ 95% confidence interval for estimating the population mean when...
Find the margin of error for a​ 95% confidence interval for estimating the population mean when the sample standard deviation equals 100 with a sample size of​ (i)484 and​ (ii)1521. What is the effect of the sample​ size?
When obtaining a confidence interval for a population mean in the case of a finite population...
When obtaining a confidence interval for a population mean in the case of a finite population of size N and a sample size n which is greater than 0.05N, the margin of error is multiplied by the following finite population correction factor Find the 95% confidence interval for the mean of 200 weights if a sample of 34 of those weights yields a mean of 155.7 lb and a standard deviation of 24.1 lb. A.148.3 lb < p < 163.1...