Final answer:
The P-value for a two-sided test with a z-score of -2.12 is approximately 0.034 after doubling the area for both tails. For a one-sided test with hypotheses H₀: μ=10 versus Hₙ: μ>10 and the same z-score, the P-value is 0.017 since there's no need to double the area for a one-sided test.
Step-by-step explanation:
The question asks to find the P-value corresponding to a test statistic for a two-sided significance test and a one-sided significance test for a population mean, given a z-score of -2.12.
For the two-sided significance test, the P-value is found by looking at both tails of the standard normal distribution. Since the test statistic is negative, we look at the left tail corresponding to z = -2.12, find that area, and then double it because it is a two-sided test. Upon using a standard normal distribution table or calculator, we would find that the area to the left of z = -2.12 is approximately 0.017. Thus, we double it to account for both tails, which gives us a P-value of approximately 0.034.
For the one-sided significance test with hypotheses H₀: μ=10 versus Hₙ: μ>10 and a negative z-score, it implies we are considering the left tail of the standard normal distribution. Since the test is one-sided, there is no need to double the area. Therefore, the P-value for this test is approximately equal to the area to the left, which is 0.017.