Using the z table, determine the critical value for the left-tailed test with α = 0.02.
To find the critical value for a left-tailed test with α = 0.02 using the standard normal (Z) distribution table, you're looking for the z-score that corresponds to an area of 0.02 to the left of it (since α represents the area in the tail).
The Z-table typically provides the area to the left of a given z-score. To find the critical value for α = 0.02, you would look in the body of the Z-table for the value closest to 0.02.
The value in the Z-table that is closest to 0.02 is typically around 0.0199 or 0.0202, depending on the table's precision.
Upon looking in the standard Z-table, you would find that the z-score corresponding to this area would be approximately -2.05 or -2.06. The negative sign indicates that this value is to the left of the mean (which is 0 for the standard normal distribution).
Thus, the critical z-value for a left-tailed test at α = 0.02 is approximately -2.05 to -2.06. You would then use this critical value to determine whether your test statistic falls into the rejection region for your hypothesis test. If your test statistic is less than or equal to -2.05 (or -2.06 depending on the exact value from your Z-table), you would reject the null hypothesis at the 0.02 significance level.