You are in charge of a poll on who is going to become the next NYC mayor. Mr X or Mr Y. You surveyed 100 people and find out that 58pp support candidate X and 42% for Y.
a. What is the sample point estimate rate of support rate for X?
b. What is the standard deviation for your point estimate above? What are the two standard deviation error bands for your point estimate ?
c. Based on your survey, what is the chance that Mr. X will lose?
d. If you want to shrink the standard deviation of your survey to 1% how many people do you need to survey?
S&P500 over the last 20 years offers a daily mean log return around 3.75 basis point and a daily standard deviation of 125 basis points.
a. Based on the sample of 20 years in 252*20=5040 days, how confident are you about the point estimate of the mean of 3.75 basis points per day? What is the range of mean with a 95% and 99% confidence?
b. What is the probability that the true mean is negative?
Note: this is asking for the lower range and upper range that will cover 95 and 99% of probability deity for the mean estimate.