If $\alpha=0.05$ in a two-tailed large-sample hypothesis test for a population mean, then
A) 1.96 is a critical value.
B) 1.96 is a $p$-value.
C) 1.65 is a $p$-value.
D) 1.65 is a critical value.

Question

Quizplus · Accepted Answer

In a two-tailed hypothesis test with $\alpha=0.05$, the critical z-values that mark the boundaries of the rejection regions in the standard normal distribution are $\pm1.96$. This is because 95% of the data falls within 1.96 standard deviations from the mean in a normal distribution, leaving 2.5% in each tail for a total of 5% ($\alpha=0.05$).

If α=0.05\alpha=0.05α=0.05 In a Two-Tailed Large-Sample Hypothesis Test for a Population Mean

If $\alpha=0.05$ In a Two-Tailed Large-Sample Hypothesis Test for a Population Mean