Using the z table in Table E of Appendix C, what are the critical values for a two-tailed test when 0.03.

Question

Using the z table in Table E of Appendix C, what are the critical values for a two-tailed test when  0.03.

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To find the critical values for a two-tailed test with a significance level of 0.03, we need to divide the alpha value by 2 (since it is a two-tailed test) and then look for the corresponding z-scores on the z-table.

The critical value for a two-tailed test with alpha/2 = 0.015 is approximately 2.17. Therefore, the critical values for the test are -2.17 and 2.17.

Looking at the z-table in Table E of Appendix C, we find that the closest z-value to 2.17 is 0.9850, and the closest z-value to -2.17 is -0.9850.

Therefore, the critical values for a two-tailed test with alpha = 0.03 are approximately -2.17 and 2.17.

The closest answer choice is B, which gives the same critical values. To find the critical values for a two-tailed test with a significance level of 0.03, we need to find the corresponding z-scores that enclose an area of 0.015 in each tail of the standard normal distribution (since it's a two-tailed test, the total area in both tails is 0.03).

Using Table E in Appendix C, we look for the row that starts with 0.01 (since the first digit of 0.03 is 0.0) and the column that corresponds to the second digit 0.015. The intersection of this row and column gives us a z-score of 2.17.

Therefore, the critical values for a two-tailed test with a significance level of 0.03 are -2.17 and 2.17 (since we need to consider both tails).

Of the given choices, only B has -2.17 and 2.17 as the critical values, so it is the best choice.

Using the Z Table in Table E of Appendix C