Question

2. We refer to a recent poll on Democratic candidates for the Presidential election 2020, among a random national sample of 1,003 adults. Results have an error margin of plus or minus 3.5 percentage points. In the poll, Joe Biden, Elizabeth Warren, and Bernie Sanders were answered to be an appropriate candidate by 27%, 21%, and 19%, respectively. Assume the level of significance, a = 5%. (a) Calculate the standard deviation of the sample. (25 pts) Note: Convert the results given in percentage points to the corresponding number of samples.

Answer 1

Marginal error= 3.5%

Standard error= 3.5/z score for a= .05

So = 3.5105/1.645= 2.133

Also number of samples = 27%+ 21%+ 19%= 67%*1003= 672.01

Standard deviation= standard error* √sample

So = 2.134*√672.01

= 55.32