Step 1 :State the null hypothesis $H_{0}$ and the alternative hypothesis $H_{1}$. The null hypothesis $H_{0}$: $p = 0.7$. The alternative hypothesis $H_{1}$: $p < 0.7$.
Step 2 :Determine the type of test statistic to use. The type of test statistic to use is a z-score.
Step 3 :Find the value of the test statistic. The value of the test statistic is -2.254.
Step 4 :Find the critical value. The critical value is -1.645.
Step 5 :Is there enough evidence to support the policy maker's claim that the proportion of residents who recycle is less than $70 \%$ ? Yes, there is enough evidence to support the policy maker's claim that the proportion of residents who recycle is less than 70%.
Step 6 :Final Answer: \(\boxed{H_{0}: p = 0.7}\), \(\boxed{H_{1}: p < 0.7}\), \(\boxed{\text{Test statistic (z-score)}: -2.254}\), \(\boxed{\text{Critical value}: -1.645}\), \(\boxed{\text{There is enough evidence to support the policy maker's claim that the proportion of residents who recycle is less than 70%}}\)