FAST Confidence Intervals and Estimation 2

Question 1

A 95% confidence interval for a population mean is (42, 58). Which statement is correct?

Accepted Answer

If we repeated sampling many times, about 95% of such intervals would contain the true mean.

Answer

A confidence interval means that 95% of intervals constructed with this method will capture the true parameter.

Question 2

Increasing the sample size while keeping confidence level constant will:

Accepted Answer

Narrow the confidence interval.

Answer

Larger samples reduce the standard error, which narrows the margin of error and tightens the interval.

Question 3

Which condition is NOT required for constructing a valid confidence interval for a population mean using the z-distribution?

Accepted Answer

The sample mean equals the population mean.

Answer

Sample means rarely equal the population mean exactly; the interval accounts for that uncertainty.

Question 4

A point estimate differs from an interval estimate in that a point estimate:

Accepted Answer

Gives a single value as the best guess for the parameter.

Answer

A point estimate is a single number used to estimate a population parameter, with no accompanying range.

Question 5

A researcher constructs a 90% confidence interval instead of a 95% confidence interval. Compared to the 95% interval, the 90% interval will be:

Accepted Answer

Narrower, because less confidence requires a smaller range.

Answer

Lower confidence levels use smaller critical z-values, producing narrower intervals.

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