A randomly-drawn survey of n=700 people asked about approval with President Biden job in office. 363 people said they approve (y=1), and 337 that they did not (y=0). Find the mean and SD of the sample, use them to estimate the mean of the sample means in repeated sampling (which is equal to the sample mean and is your estimate of the true population mean) and the standard error of the means in repeated sampling (we divide the SD by sqrt of n observations). Finally, construct a 95 per cent confidence interval of where the true mean of the President's approval lies (i.e. the approval of the entire population of people in the US).

Now, redo the calculations for a survey with 2500 respondents, of whom 1296 approve of him. Do your conclusions about how many Americans approve of his performance change in any meaningful way?