Step 1 :Given that the number of voters who said they'd vote for Brown is 149 and the total number of voters surveyed is 400, we can calculate the sample statistic for the proportion of voters surveyed who said they'd vote for Brown by dividing the number of voters who said they'd vote for Brown by the total number of voters surveyed. This will give us a decimal representation of the proportion.
Step 2 :\[\frac{149}{400} = 0.3725\]
Step 3 :To estimate the number of the 11300 registered voters who might vote for Brown, we can multiply the sample statistic by the total number of registered voters.
Step 4 :\[0.3725 \times 11300 = 4209.25\]
Step 5 :Since the number of voters cannot be a decimal, we round it to the nearest whole number.
Step 6 :\[\text{Rounded number of voters} = \text{round}(4209.25) = 4209\]
Step 7 :Final Answer: The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is \(\boxed{0.3725}\). This suggests that we might expect approximately \(\boxed{4209}\) of the 11300 registered voters to vote for Brown.