Final answer:
The standard error of the sample proportion is approximately 0.0306.
Step-by-step explanation:
The standard error of a sample proportion can be calculated using the formula:
Standard Error = √((p)(1-p)/n)
where p is the proportion of the sample and n is the sample size. In this case, the proportion is 0.25 (since 25% of the sample is strongly opposed to having a state lottery) and the sample size is 200. Plugging these values into the formula:
Standard Error = √((0.25)(1-0.25)/200) = √(0.1875/200) = √(0.0009375) = 0.0306
So, the standard error of the sample proportion is approximately 0.0306.