Find the critical value for constructing the following confidence interval. $90 \%$ t-interval with $\mathrm{n}=4$ The critical value from the t-distribution is $\square$. (Round to three decimal places as needed.)
Solution
Step 1 ：We are given a 90% t-interval with n=4. We need to find the critical value for constructing the confidence interval.
Step 2 ：The degrees of freedom is calculated as n-1, which is 4-1=3.
Step 3 ：The confidence level is 90%, so the significance level is 1-0.90=0.10. Half of this value, 0.05, is in each tail of the t-distribution.
Step 4 ：We need to find the t-value that corresponds to this in the t-distribution table. This can be done using the scipy library's t.ppf function.
Step 5 ：Using the t.ppf function with the quantile as 0.05 and the degrees of freedom as 3, we get the t-value as approximately 2.353.
Step 6 ：This t-value is the critical value for constructing the confidence interval.
Step 7 ：Final Answer: The critical value from the t-distribution is \( \boxed{2.353} \).
