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Which statement regarding confidence intervals is TRUE?Group of answer choicesA 95% confidence interval produced from different data to a 99% confidence interval will likely be narrower.A 95% confidence interval produced from the same data as a 99% confidence interval will likely be wider.A 95% confidence interval produced from the same data as a 99% confidence interval will likely be narrower.A specific 95% confidence interval is the probability that a population parameter of interest falls within a specified range.

Question

Which statement regarding confidence intervals is TRUE?Group of answer choicesA 95% confidence interval produced from different data to a 99% confidence interval will likely be narrower.A 95% confidence interval produced from the same data as a 99% confidence interval will likely be wider.A 95% confidence interval produced from the same data as a 99% confidence interval will likely be narrower.A specific 95% confidence interval is the probability that a population parameter of interest falls within a specified range.

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Solution

The correct statement regarding confidence intervals is: "A 95% confidence interval produced from the same data as a 99% confidence interval will likely be narrower."

Here's why:

A confidence interval is a range of values, derived from a statistical procedure, that is likely to contain the value of an unknown parameter. The width of the confidence interval gives us some idea about how uncertain we are about the unknown parameter. A wider interval may indicate that we are less certain about the value of the parameter.

A 95% confidence interval means that we are 95% confident that the true population parameter lies within the interval. A 99% confidence interval means we are 99% confident that the true population parameter lies within the interval.

The key point here is that to be more confident that we have captured the true parameter, we need to cast a wider net, i.e., we need a wider interval. Therefore, a 99% confidence interval will be wider than a 95% confidence interval produced from the same data.

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Similar Questions

Examine the following statements and then select the one statement that is correct.Group of answer choicesA wider confidence interval means less confidence in the estimate (all other things being equal).A narrower confidence interval is always better than a wider confidence interval.For a 95% confidence interval for a population mean, there is a 95% chance that the confidence interval includes the sample mean.The width of a confidence interval is affected by both the sampling error and the required level of confidence.

For confidence interval estimates, which of the following statements is FALSEGroup of answer choicesincreasing the sample size decreases the width of the confidence intervalusing a sample standard deviation instead of the population standard deviation always results in a wider confidence intervalthe width of the confidence interval increases as we demand more confidencea 95% confidence interval for the mean (with population standard deviation known) will be narrower than a 99% confidence interval

Suppose (35,40) is a 95% confidence interval estimate for a population mean 𝜇. Which of the following are true statements?I. There is a .95 probability that 𝜇 is between 35 and 40.II. If 100 random samples of the given size are picked and a 95% confidence interval is calculated from each, then 𝜇 will be in 95 of the resulting intervals.III. If 95% confidence intervals are calculated from all possible samples of the given size, 𝜇 will be in 95% of these intervals.I and III and IIIII and IIII, II, and IIINone of the above gives the complete set of true responses.

Which set of circumstances is most likely to result in a wide confidence interval?Question 10Answera.large n and a confidence level of .99b.large n and a confidence level of .95c.small n and a confidence level of .95d.small n and a confidence level of .99

What does a 95% confidence interval for a mean suggest?Question 3Answera.The mean will increase by 95%.b.There is a 95% chance of replicating the study results.c.95% of the sample mean lies within the interval.d.95% of the population mean is expected to lie within the interval.

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