Which is a critical value for a two-tailed t-test when α = 0.02 and the sample size is 19?
To find the critical value for a two-tailed t-test when the significance level (α) is 0.02 and the sample size (n) is 19, you need to find the t value from the t-distribution table that corresponds to a confidence level of 1 - α and with degrees of freedom (df) equal to n - 1.
Since we have 19 samples:
Degrees of freedom (df) = n - 1 = 19 - 1 = 18
For a two-tailed test, the significance level on each tail will be α/2 because you're dividing the α level between two tails (the upper and the lower tail of the distribution).
Therefore, α/2 = 0.02 / 2 = 0.01
Now you need to look up the critical value associated with α/2=0.01 (or the 99% confidence level) and 18 degrees of freedom in a t-distribution table. Alternatively, you could use statistical software or an online calculator to find it.
Since I don't have a t-table to hand right now, and assuming you're looking for an approximation, I can provide you with a general method to find an approximate value of a critical t value: using the inverse cumulative distribution function (CDF) of the t-distribution, which is used in many statistical software packages like R or Python’s SciPy library.
Using Python's SciPy library, the calculation would look something like this:
```python
from scipy.stats import t
# Set your significance level and degrees of freedom
alpha = 0.02
df = 18
# For two-tailed tests, we split the alpha in half
critical_value = t.ppf(1 - alpha / 2, df)
print(critical_value)
```
This script will output the critical t value for a two-tailed t-test with α = 0.02 and degrees of freedom of 18. You should interpret this value in the context of a two-tailed t-test, meaning that the absolute value of your test statistic needs to be greater than this critical value for the result to be statistically significant at the 0.02 level.
Remember, the actual critical value could be slightly different depending on the exactness of t-distribution tables or specific statistical software's implementation of the inverse CDF function.