Questions: Here are summary statistics for the weights of Pepsi in randomly selected cans: n=36, x̄=0.82411 lb, s=0.00567 lb. Use a confidence level of 95% to complete parts (a) through (d) below. a. Identify the critical value t(α / 2) used for finding the margin of error. To determine the critical value t(α / 2), first determine the value of α for a 95% confidence level. α= (Type an integer or a decimal. Do not round.)

Solution Steps

For a confidence level of \( 95\% \), we calculate \( \alpha \) as follows: \[ \alpha = 1 - 0.95 = 0.05 \]

Using the calculated \( \alpha \), the critical value \( t_{\alpha/2} \) is determined. For a \( 95\% \) confidence level, the critical value is: \[ t_{\alpha/2} \approx 1.96 \]

The margin of error \( E \) is calculated using the formula: \[ E = z \cdot \frac{s}{\sqrt{n}} \] Substituting the values: \[ E = 1.96 \cdot \frac{0.00567}{\sqrt{36}} \approx 0.0019 \]

The confidence interval for the mean is given by: \[ \bar{x} \pm E \] Substituting the sample mean \( \bar{x} = 0.8241 \) and the margin of error \( E \): \[ 0.8241 \pm 0.0019 \] This results in the confidence interval: \[ (0.8223, 0.826) \]

Final Answer