Part CCSIR NET December 2023one-sided-intervals

One sided intervals

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

A. $(\overset{ˉ}{X} - (S / n)$ $t_{n - 1, 0.05}$ , $\overset{ˉ}{X} + (S / n)$ $t_{n - 1, 0.05})$
B. $(\overset{ˉ}{X} - (σ / n)$ $z_{0.05}$ , $\overset{ˉ}{X} + (σ / n)$ $z_{0.05})$
C. $[\overset{ˉ}{X} - (S / n)$ $t_{n - 1, 0.9}$ , $\infty)$
D. $(- \infty, \overset{ˉ}{X} - (S / n)$ $t_{n - 1, 0.9})$

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Boundary and endpoint

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One sided intervals

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