more statistics questions

Project Description:

problem 1: what is the upper bound of the 95% confidence interval for the proportion of individuals whose favorite sport is basketball using the normal approximation? report 3 decimals. there are 17 out of 109 individuals whose favorite sport is basketball, so i believe the proportion is 0.15596? correct me if i am wrong. my guess as to the upper confidence interval bound is 0.235

problem 2: for the t-distribution, the smaller n is, the less variability in the t. my guess is true. am i correct or incorrect?

problem 3: relating to problem 1, in doing a larger survey, how many individuals should you survey to estimate the fraction of students whose favorite sport is basketball, p, to within 0.02 with 90% confidence, using the estimate from problem 1 for p?
a. 883
b. 910
c. 857
d. 950
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