Part CCSIR NET December 2023one-sided-intervals

One sided intervals

For n ≥ 2, let $X_{1}, \dots, X_{n}$ be from $N(\mu, \sigma^{2})$ with both unknown, X̄ the mean and $S^{2}$ the sample variance. With $z_\alpha$ and $t_{m,\alpha}$ the $(1 - \alpha)-$ th quantiles, which of the following represent 90% confidence intervals for $\mu$ ?

A. $({\bar{X}} - (S/\sqrt{n})$ $t_{n-1,0.05}$ , ${\bar{X}} + (S/\sqrt{n})$ $t_{n-1,0.05})$ ✓ Correct
B. $({\bar{X}} - (\sigma/\sqrt{n})$ $z_{0.05}$ , ${\bar{X}} + (\sigma/\sqrt{n})$ $z_{0.05})$
C. $[{\bar{X}} - (S/\sqrt{n})$ $t_{n-1,0.9}$ , $\infty)$
D. $(-\infty, {\bar{X}} - (S/\sqrt{n})$ $t_{n-1,0.9})$ ✓ Correct

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests boundary and endpoint.

See pricing

50 are analysed free — try those first.

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

One sided intervals

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