Find the critical value(s) for a left-tailed $z$-test with $\alpha=0.02$. Include a graph with your answer.
The critical value(s) is(are)
(Round to two decimal placearas needed. Use a comma to separate answers as needed.)
Answer
Final Answer: The critical value for a left-tailed z-test with \(\alpha=0.02\) is approximately \(\boxed{-2.05}\).
Step 1 ：Given that the significance level, \(\alpha\), is 0.02 for a left-tailed z-test.
Step 2 ：We need to find the critical value, which is the z-score below which we find a total probability of 0.02.
Step 3 ：We can find this value using the percent point function (ppf), which is the inverse of the cumulative distribution function (cdf). The ppf gives the value of the variable for a given percentile.
Step 4 ：By calculating, we find that the critical value is approximately -2.053748910631823.
Step 5 ：Rounding to two decimal places, the critical value is -2.05.
Step 6 ：Final Answer: The critical value for a left-tailed z-test with \(\alpha=0.02\) is approximately \(\boxed{-2.05}\).
