Using the z table, which is a critical value for a two-tailed test when α = 0.03?
Question 15 options:
1)
1.88
2)
-2.17
3)
2.05
4)
-2.33
A two-tailed test with α = 0.03 means that the significance level on each tail of the normal distribution is 0.015 (because 0.03/2 = 0.015). Thus, we are looking for the z-score that corresponds to the cumulative probability of 0.5 + 0.015 = 0.515 for the upper tail and 0.5 - 0.015 = 0.485 for the lower tail.
To find the critical values (z-scores), you'd normally look these up in the z-table or use statistical software. Since I don't have access to real-time computational tools, but based on the commonly used z-scores for standard normal distribution, we can closely estimate the values.
Option 1: 1.88 - It corresponds to a cumulative probability slightly below 0.03 for a one-tailed test or 0.06 for a two-tailed test. This is quite close but usually corresponds to a confidence level around 95 to 96%.
Option 2: -2.17 - This would generally correspond to a cumulative probability lower than 0.015 from the lower tail of the distribution, so this is not the right value for α = 0.03.
Option 3: 2.05 - This is very close and indeed is the right critical value for a two-tailed test with approximately 0.02 to 0.03 significance level, which makes it likely the correct answer.
Option 4: -2.33 - This corresponds to a cumulative probability lower than 0.01 in the lower tail, making it too extreme for our α = 0.03.
Out of the options given and considering the standard z-table values, the critical value for a two-tailed test when α = 0.03 is most likely:
3) 2.05
It's crucial to note that in practice, you should look up the precise critical values using a z-table or statistical software to ensure accuracy.