For an upper-tail hypotheses about a population mean with σ known and α=5%, which one is the rejection region?

Question

BlackTom AI · Accepted Answer

When testing a population mean with known sigma and an upper-tailed test at alpha = 0.05, we use a z-test and look for the critical z value that leaves 5% in the upper tail.
Option 1: z>=1.96. This threshold corresponds to a two-tailed test at alpha = 0.05 (cutoffs at ±1.96) rather than a one-tailed upper-tail test, so it’s not correct for this scenario.
Option 2: z<=1.645. This uses a lower-tail criterion (rejecting for very small z-values), which is the opposite of what an upper-tail test requires, so this is incorrect.
Option 3: z>=1.645. This matches the standard critical value for a one-tailed z-test at alpha = 0.05 with known sigma, since the right tail beyond 1.645 accounts for the 5% rejection region in an upper-tail test.
Option 4: t>=1.96. The t-distribution is used when sigma is unknown and the sample size is small; with known sigma (as stated) we should use z, not t, and 1.96 is the two-tailed cutoff, not appropriate here. Hence this option is incorrect.

For an upper-tail hypotheses about a population mean with σ known and α=5%, which one is the rejection region?单项选择题

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