Question

What sample statistic provides the best interval estimate of the population mean (u) when the population variance is NOT known?

1) Xbar +/- (Z)(Sxbar)
2) Xbar +/- (t) (population mean xbar)
3) Xbar +/- (Z) (population mean xbar)
4) X bar +/- (t) (Sxbar)

Answer 1

Option 4) X bar +/- (t) (Sxbar) provides the best interval estimate of the population mean (μ) when the population variance is not known.

Step-by-step explanation:

The sample statistic that provides the best interval estimate of the population mean (μ) when the population variance is not known is option 4) X bar +/- (t) (Sxbar).

When the population variance is unknown, we use the Student's t-distribution to calculate the confidence interval. This is because the normal distribution is less accurate when using the sample standard deviation as an estimate.

The general form for a confidence interval for a single mean, population standard deviation unknown, Student's t is given by (lower bound, upper bound) = (point estimate – EBM, point estimate + EBM).