Final answer:
The standard deviation of the sample proportion decreases as the sample size increases, and it is unknown without knowing the population proportion.
Step-by-step explanation:
The standard deviation of the sample proportion when the sample size n is large enough actually decreases. When we are dealing with a large sample size, the distribution of the sample proportion is approximately normal, and its standard deviation can be calculated using the formula √[p(1-p)/n], where p is the population proportion and n is the sample size. Therefore, without the population proportion p, the standard deviation of the sample proportion is unknown. As the sample size increases, the standard deviation of the sample proportion decreases, which means that you can be more confident that the sample proportion is close to the true population proportion.