Find $\hat{p}$ and $\hat{q}$. Round your answers to three decimal places. \[ n=145 \text { and } X=81 \]

Step 1 ：Given that the total number of trials, n = 145 and the number of successful outcomes, X = 81.

Step 2 ：The sample proportion, \(\hat{p}\), is calculated by dividing the number of successful outcomes (X) by the total number of trials (n).

Step 3 ：So, \(\hat{p}\) = \(\frac{X}{n}\) = \(\frac{81}{145}\) = 0.5586206896551724.

Step 4 ：The proportion of unsuccessful outcomes, \(\hat{q}\), is calculated as 1 - \(\hat{p}\).

Step 5 ：So, \(\hat{q}\) = 1 - \(\hat{p}\) = 1 - 0.5586206896551724 = 0.4413793103448276.

Step 6 ：Rounding these values to three decimal places, we get \(\hat{p}\) = 0.559 and \(\hat{q}\) = 0.441.

Step 7 ：Final Answer: The values of \(\hat{p}\) and \(\hat{q}\) are \(\boxed{0.559}\) and \(\boxed{0.441}\) respectively.