Answer :
We are asked to compute the pooled proportion
[tex]$$
\hat{p}_{c} = \frac{x_1+x_2}{n_1+n_2}.
$$[/tex]
Step 1: Add the number of successes in both samples:
[tex]$$
x_1 + x_2 = 80 + 70 = 150.
$$[/tex]
Step 2: Add the sample sizes:
[tex]$$
n_1 + n_2 = 200 + 300 = 500.
$$[/tex]
Step 3: Calculate the pooled proportion by dividing the totals:
[tex]$$
\hat{p}_{c} = \frac{150}{500} = 0.3.
$$[/tex]
Step 4: Express the answer to 3 decimal places:
[tex]$$
\hat{p}_{c} = 0.300.
$$[/tex]
Thus, the final answer is [tex]$\hat{p}_{c} = 0.300$[/tex].
[tex]$$
\hat{p}_{c} = \frac{x_1+x_2}{n_1+n_2}.
$$[/tex]
Step 1: Add the number of successes in both samples:
[tex]$$
x_1 + x_2 = 80 + 70 = 150.
$$[/tex]
Step 2: Add the sample sizes:
[tex]$$
n_1 + n_2 = 200 + 300 = 500.
$$[/tex]
Step 3: Calculate the pooled proportion by dividing the totals:
[tex]$$
\hat{p}_{c} = \frac{150}{500} = 0.3.
$$[/tex]
Step 4: Express the answer to 3 decimal places:
[tex]$$
\hat{p}_{c} = 0.300.
$$[/tex]
Thus, the final answer is [tex]$\hat{p}_{c} = 0.300$[/tex].
