Answer and explain. If all other quantities remain the same, what will happen to the width of a confidence interval if there is an increase in the: confidence level; sample size; and standard deviation
General form of a confidence interval (CI):
A confidence interval estimates are intervals within which the parameter is expected to fall, with a certain degree of confidence.
The general form:
estimate ± critical value × std.dev of the estimate
or estimate ± margin of error
(a) An increase in the level of confindence , increases the confidence interval (because in this case critical value increases).
(b)An increase in the sample size , decreases the confidence interval (because in this case standard error decreases).
(c) An increase in the population standanard deviation , increases the confidence interval (because in this case standard error /deviation of estimate increases).
What will happen to the width of a confidence interval if there is an increase in the: confidence level, sample size, and standard deviation?
What happens to the width of a confidence interval if the sample size increases, but all other quantities involved (e.g., the coverage probability and population variance) remain fixed? Please provide both an intuitive and mathematical explanation of your answer
D5: What happens to the width of your confidence interval as you increase your sample size? a. Why does this happen? b. Provide a real world example that explains this concept. c. Find an example in your homework this week that illustrates increasing the sample size and how it changes the width of the confidence level. Provide both the question statement and the solution.
QUESTION 1 Suppose we have a sample size of 100 and calculate a confidence interval. What will happen to that interval if we then get a sample size of 200 (all else equal). It will become narrower It will become wider. It will remain the same, because the mean is not changing It will get closer to 1.96. QUESTION 1 Suppose we have a sample size of 100 and calculate a confidence interval. What will happen to that interval if...
Increasing the confidence level of your confidence interval will have what effect on the width of the interval? It is impossible to tell. The width will decrease. The width will remain the same. The width will increase.
Which of the following correctly describes how the width of a confidence interval for a population mean changes when the population standard deviation is known? There is no change if just the sample size increases. The interval widens if the sample size stays the same and confidence level decreases. The interval narrows if the sample size increases and confidence level stays the same. The interval narrows if the sample size decreases and confidence level stays the same. The interval widens...
Which of the following does NOT correctly describe how the width of a confidence interval for a population mean changes when the population standard deviation is known? The interval changes if the sample size decreases. The interval changes if the sample size increases. The interval narrows if the sample size increases and confidence level stays the same. The interval widens if the sample size decreases and the confidence level stays the same. The interval widens if the sample size stays...
Use the one-mean t-interval procedure with the sample mean, sample size, sample standard deviation, and confidence level given below to find a confidence interval for the mean of the population from which the sample was drawn. sample mean=3.0 n=41 s=5.4 confidence level=90% The 90% confidence interval about μ is ?? to ???
Use the one-mean t-interval procedure with the sample mean, sample size, sample standard deviation, and confidence level given below to find a confidence interval for the mean of the population from which the sample was drawn. x̄=4.0 n=61 s=6.1 confidence level =99% The 99% confidence interval about μ is ??? to ??? (Round to four decimal places as needed.)
If the sample mean and sample standard deviation are the same when doing a study with an unknown mean and standard deviation of the population. What effect does increasing the sample size have on The P value and the margin of error (assuming the same confidence level)? Also, what effect does increasing the sample size have on the width of the confidence interval (assuming the same confidence level)?
For confidence interval computations, if the sample size is increased, we expect the margin of error to: a. Increase b. Decrease c. stay the same The company you work for produces automotive parts for GM. A certain machine that makes a cutout in a piece of steel averages a cut size of 203.2085 mm with a standard deviation of 0.2083 mm. A random sample of 66 is taken from the population. What is the distribution of the sample mean? Approximately...