Which are true about confidence intervals A. A 95% confidence interval is always

Question

Which are true about confidence intervals

A. A 95% confidence interval is always wider than a 90% confidence interval.

B. You can construct a confidence interval around a percent defective.

C. When constructing a confidence interval around a mean and the standard deviation of the population is known / sqrt(n) is used to estimate the standard deviation of the distribution to xbar.

D. As the sample size increases the confidence interval gets smaller.

E. You can have a one sided or two sided confidence interval.

F. As xbar increased the width of the CI increase.

G. The z value used in the calculation of a confidence interval around a mean is the number of standard deviations.

H. If known, as the variance of the population increases the interval gets smaller.

I. As the sample size increases the probability that the interval contains the sample mean decreases.

J. If the population variance is unknown it is always ok to use the standard deviation of the sample (s) as an estimate and use the z value to construct the CI.

K. You can construct a confidence interval around a difference in two population means.

L. As xbar decrease the width of the CI increases.

M. If 90% and 95% confidence interval are calculated using the same test statistic, the 95% confidence interval is more likely to contain the true mean.

N. You can construct a confidence interval around a population standard deviation.

O. By definition if an infinite number of samples were drawn from a population and 90% confidence intervals were calculated using the test statistic, 90% of the calculated confidence interval would contain the population parameter that the test statistic estimated.

P. If the population variance is unknown and the sample size (n) is less than 40, use the standard deviation of the sample (s) as an estimate of and use the t value to construct the CI.

Explanation / Answer

Answer to the question)

Part a)

true

Width of confidence interval depends on MArgin of error

Formula of Margin of Error = z * s/sqrt(n)

As confidence level decreases from 95% to 90% , the value of Z also decreases from 1.96 to 1.645

Thus the margin of error also decreases

Thus as the confidence level decreases from 95% to 90% , the width of the itnerval also decreases.

Thus statement A is TRUE

.

Part b)

We construct a confidence interval around the mean , thus this statement is FALSE

.

Part c)

Yes this is u, when the standard deviation of the populaton is known , it helps us find the standard error of the sample mean x bar . The value of standard error is SE = Sigma / sqrt(n)

.

Part d)

Width of the interval depends on the margin of error

Formula of margin of error = z* s/ sqrt(n)

thus if the sample size increases, the value of margin of error decreases

if margin of error decreases, the width of the interval also decreases

Thus this statement is TRUE

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