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
Question
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
Solution
The false statement is: "using a sample standard deviation instead of the population standard deviation always results in a wider confidence interval."
Here's why:
While it's true that using a sample standard deviation can often result in a wider confidence interval (because the t-distribution is wider than the normal distribution), this is not always the case. The width of the confidence interval also depends on the sample size. If the sample size is large, the sample standard deviation can be a very good estimate of the population standard deviation, and the confidence interval may not be much wider than if the population standard deviation were used. In fact, for large sample sizes, the t-distribution approaches the normal distribution, so the difference between the two becomes negligible.
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.
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.
Suppose you compute a confidence interval with a sample size of 81. What will happen to the confidence interval if the sample size increases to 84?The confidence interval will widen.The confidence interval will narrow.The width of the confidence interval will stay the same.
Changing from a 95% confidence interval estimate for a population proportion to a 99% confidence interval estimate, with all other things being equalSelect one:a. Decreases the interval size by 4%b. Increases the interval size by 4%c. Increases the interval size by 31%d. Decreases the interval size by 31%e. This question cannot be answered without knowing the sample size
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
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