Question

select the correct statement. a.) the critical z-score for a right-tailed test at a 9% significance level is 1.34. b.) the critical z-score for a two-sided test at a 4% significance level is 1.75. c.) the critical z-score for a two-sided test at a 20% significance level is 0.85. d.) the critical z-score for a left-tailed test at a 12% significance level is -0.45.

Answer 1

The correct statement about critical z-scores is that the critical z-score for a right-tailed test at a 9% significance level is 1.34, as mentioned in Option A. The other options provide incorrect critical z-scores for the stated significance levels and types of tests.

Step-by-step explanation:

The question is about selecting the correct statement regarding critical z-scores for different types of hypothesis tests at various significance levels. A critical z-score is the z-value beyond which we would consider the results statistically significant for a given significance level in a normal distribution.

Option A suggests that the critical z-score for a right-tailed test at a 9% significance level is 1.34. However, using the standard normal distribution table or a Z-score calculator, we find that the critical z-score for a 9% right-tailed test (which corresponds to a 91% confidence level) is approximately 1.34, confirming that this statement is correct.

Option B suggests a critical z-score of 1.75 for a two-sided test at a 4% significance level. However, for a two-sided test at a 4% significance level (which corresponds to a 96% confidence level), the critical z-score would actually be higher. We would look at the z-scores for a 98% confidence level (since half of 4% would be in each tail) which is approximately 2.33, not 1.75.

Option C suggests a critical z-score of 0.85 for a two-sided test at a 20% significance level. The critical z-score for a two-sided test at a 20% significance level should reflect the 90% confidence level (100% - 20% = 80%, with 90% in the middle since it's two-sided). For this, the critical z-scores would be approximately ±1.645, which is significantly higher than 0.85.

Option D suggests that the critical z-score for a left-tailed test at a 12% significance level is -0.45. But for a left-tailed test at a 12% significance level, we would expect a critical z-score more negative than -1.17 as it would correspond to the bottom 12% of the distribution.

Therefore, the correct statement is Option A.