Question

Consider the hypotheses below.

H0​: μ=50
H1​: μ≠50
Given that x=55, s=8​, n=250, and α=0.01​, answer the questions
below.
1. The critical​ value(s) is(are)?

Answer 1

The critical values for the given hypothesis test with α=0.01 are approximately ±Z≈2.33, based on the z-distribution tables.

Step-by-step explanation:

The given hypotheses for a statistical test are H0: μ=50 and H1: μ≠50. To find the critical value(s) for this two-tailed test, we need to use the z-distribution since the population variance is known. Given the significance level (α) of 0.01, this means the critical values will be the z-scores that correspond to the upper and lower 0.5% of the z-distribution, because a two-tailed test splits the significance level between the two tails. Thus, the critical z-values are ±Z.

Z tables or calculators would show that the critical z-values are approximately ±Z≈2.33. Hence, the critical values are ±Z≈2.33.