Final answer:
Critical z-scores for hypothesis tests are determined by the tail type and significance level, using a z-table or statistical software. The values in the student's question do not correctly correspond to the given significance levels.
Step-by-step explanation:
To calculate the critical z-score for hypothesis tests, you have to consider whether the test is left-tailed, right-tailed, or two-tailed and what the significance level (alpha, α) is. For a right-tailed test with an 18% significance level, you would look in the z-table for the value that corresponds to an area of 1 - 0.18 in the left tail, which is not the 0.57 mentioned in the question. Similarly, for a left-tailed test at a 14% significance level, find the z-score that corresponds to an area of 0.14 in the left tail, which again is different from -1.08 as per the question.
For a two-tailed test, the significance level is split between the two tails of the distribution. At an 18% significance level, each tail would have 9% of the alpha level, and you'd look for the z-score that has 0.09 in the right tail for the positive critical value and -0.09 in the left tail for the negative critical value. The critical z-scores would be the absolute values to the right and left that accumulate 0.91 and 0.09 of the area under the curve, respectively, and not 1.95 as stated. For a two-tailed test at a 10% level, 5% would be in each tail, so the critical values would be the z-scores that have 0.95 and 0.05 in the left tail, which differ from 1.23. Correct values must be found by locating the area in the z-table corresponding to 1 minus the significance level for right-tailed tests, and the significance level itself for left-tailed tests.
To determine the correct critical z-scores, you would typically use a z-table or statistical software. Critical z-scores correspond to the specific tail areas denoted by the significance level. For example, a z-score critical value of -1.645 would be used for a left-tailed test with α = 0.05, indicating that 5% of the area under the normal distribution curve lies to the left of this z-score.