Confidence Intervals and Estimation Flashcards
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A 95% confidence interval for a population mean is (42, 58). Which statement is correct?
Answer: If we repeated sampling many times, about 95% of such intervals would contain the true mean.
A confidence interval means that 95% of intervals constructed with this method will capture the true parameter.
Increasing the sample size while keeping confidence level constant will:
Answer: Narrow the confidence interval.
Larger samples reduce the standard error, which narrows the margin of error and tightens the interval.
Which condition is NOT required for constructing a valid confidence interval for a population mean using the z-distribution?
Answer: The sample mean equals the population mean.
Sample means rarely equal the population mean exactly; the interval accounts for that uncertainty.
A point estimate differs from an interval estimate in that a point estimate:
Answer: Gives a single value as the best guess for the parameter.
A point estimate is a single number used to estimate a population parameter, with no accompanying range.
A researcher constructs a 90% confidence interval instead of a 95% confidence interval. Compared to the 95% interval, the 90% interval will be:
Answer: Narrower, because less confidence requires a smaller range.
Lower confidence levels use smaller critical z-values, producing narrower intervals.
The margin of error in a confidence interval is defined as:
Answer: Half the width of the confidence interval.
The margin of error equals the critical value multiplied by the standard error, which is half the total interval width.
To reduce the margin of error by half while keeping the confidence level the same, you must:
Answer: Quadruple the sample size.
Since margin of error is proportional to 1/√n, halving it requires multiplying n by 4.