Here are summary statistics for the weights of Pepsi in randomly selected cans: $n=36, \bar{x}=0.82409 \mathrm{lb}, s=0.00573 \mathrm{lb}$. Use a confidence level of $95 \%$ to complete parts (a) through (d) below.
a. Identify the critical value tys used for finding the margin of error.
\[
\mathrm{t}_{\alpha / 2}=
\]
(Round to two decimal places as needed.)
Answer
Final Answer: The critical value \(t_{\alpha / 2}\) used for finding the margin of error is \(\boxed{2.03}\).
Step 1 ：The critical value t is used in a t-distribution to find the margin of error. The t-distribution is used when the population standard deviation is unknown and the sample size is small.
Step 2 ：The critical value t is found by looking up the confidence level and degrees of freedom in a t-distribution table. In this case, the confidence level is 95% and the degrees of freedom is n-1 = 36-1 = 35.
Step 3 ：The critical value for t is 2.03.
Step 4 ：Final Answer: The critical value \(t_{\alpha / 2}\) used for finding the margin of error is \(\boxed{2.03}\).
