For $X_{1}=38, n_{1}=61, X_{2}=22$, and $n_{2}=69$, find $\bar{p}$ and $\bar{q}$. Round your answers to 3 decimal places as needed. \[ \bar{p}=\square, \bar{q}= \]

Step 1 ：Given that $X_{1}=38, n_{1}=61, X_{2}=22$, and $n_{2}=69$, we are asked to find the values of $\bar{p}$ and $\bar{q}$.

Step 2 ：In statistics, $\bar{p}$ and $\bar{q}$ represent the sample proportions. The formula for a sample proportion is $\bar{p} = \frac{X}{n}$, where $X$ is the number of successes and $n$ is the total number of trials.

Step 3 ：Using the given values, we can calculate $\bar{p}$ and $\bar{q}$ as follows:

Step 4 ：For $\bar{p}$, we use $X_{1}$ and $n_{1}$, so $\bar{p} = \frac{X_{1}}{n_{1}} = \frac{38}{61} = 0.6229508196721312$.

Step 5 ：For $\bar{q}$, we use $X_{2}$ and $n_{2}$, so $\bar{q} = \frac{X_{2}}{n_{2}} = \frac{22}{69} = 0.3188405797101449$.

Step 6 ：Rounding these values to three decimal places, we get $\bar{p} = 0.623$ and $\bar{q} = 0.319$.

Step 7 ：So, the final answer is $\bar{p} = \boxed{0.623}$ and $\bar{q} = \boxed{0.319}$.