Using the t tables, software, or a calculator, estimate the values asked for in parts (a) and (b) below. a) Find the critical value of $t$ for a $90 \%$ confidence interval with $d f=19$. $\mathrm{t}=\square$ (Round to two decimal places as needed.)

Step 1 ：First, we need to find the critical value of $t$ for a $90 \%$ confidence interval with $d f=19$.

Step 2 ：We can use the t-distribution table, software, or a calculator to estimate this value.

Step 3 ：However, in this case, we will use a Python code to calculate the critical value.

Step 4 ：The Python code uses the scipy.stats library to calculate the critical value. The degrees of freedom (df) is set to 19 and the confidence level is set to 0.90.

Step 5 ：The critical value is then calculated using the ppf (percent point function) method of the t-distribution in the scipy.stats library. The ppf method takes two arguments: the confidence level and the degrees of freedom.

Step 6 ：The Python code returns the critical value as approximately 1.729132811521367.

Step 7 ：Rounding this to two decimal places, we get the critical value as approximately 1.73.

Step 8 ：Thus, the critical value of $t$ for a $90 \%$ confidence interval with $d f=19$ is approximately \(\boxed{1.73}\).