What happens to confidence intervals when you increase the level of confidence (or equivalently decrease the level of significance)?Select all that applyGroup of answer choicesConfidence intervals get narrowerConfidence intervals get widerWe are more confident that the true population mean is inside the intervalsWe are less confident that the true population mean is inside the intervals
Question
What happens to confidence intervals when you increase the level of confidence (or equivalently decrease the level of significance)?Select all that applyGroup of answer choicesConfidence intervals get narrowerConfidence intervals get widerWe are more confident that the true population mean is inside the intervalsWe are less confident that the true population mean is inside the intervals
Solution
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Confidence intervals get wider: As the level of confidence increases, the confidence interval also increases or gets wider. This is because a higher level of confidence means that we want to be more sure that we are capturing the true population parameter, so we need a wider interval.
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We are more confident that the true population mean is inside the intervals: Increasing the level of confidence means that we are more sure that the true population mean lies within our confidence interval. For example, a 95% confidence interval means that we are 95% confident that the true population mean is within our interval. If we increase this to a 99% confidence interval, we are now 99% confident that the true population mean is within our interval.
The other two options are incorrect. Confidence intervals do not get narrower with increased confidence level, and we do not become less confident that the true population mean is inside the intervals.
Similar Questions
Lowering the Confidence Level will have what effect on the Confidence Interval?Group of answer choicesConfidence Interval will be unchangedConfidence Interval will get smallerConfidence interval will be less likely to be wrongConfidence Interval will get larger
The width of a confidence interval increases as the level of significance increases.Group of answer choicesTrueFalse
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
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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