Using the z table, which is a critical value for a two-tailed test when α = 0.03?
To find the critical value for a two-tailed test with α = 0.03 using the z-table, you need to split the alpha value in half because there are two tails in the test, and you're distributing the alpha equally between them. So, each tail will have an α/2 = 0.03/2 = 0.015 significance level.
Now, you will look up the z-value that corresponds to 0.015 in the upper tail of the standard normal distribution (since most standard z-tables give the area to the left of the z-score).
Since z-tables may vary slightly in how they present information, you might have to use the value that corresponds to an area to the left of the z-score equal to 1 - 0.015 = 0.985. This is because we want the z-score that leaves 0.015 to the right.
Looking up the value in the z-table that corresponds to a cumulative probability close to 0.985, you will find that the z-score is approximately 2.17.
Therefore, the critical value z* for a two-tailed test with a significance level of α = 0.03 is approximately ±2.17. This means that if your z-statistic is greater than 2.17 or less than -2.17, you would reject the null hypothesis for this two-tailed test.