Question

When 255 college students are randomly selected and surveyed, it is found that 111 own a car. find the best point estimate for a 99% confidence interval for the true proportion of all college students who own a car. round your answer to the ten-thousandth decimal place?

Answer 1

Sample size, N = 255 students
Number of those owning a car = 111
Z at 99% confidence = 2.58

Now,
Point estimate, p = 111/255 = 0.43529

True proportion = p+/- Z*Sqrt [p(1-p)/N] = 0.43529 +/- 2.58*Sqrt[0.43529(1-0.43529)/255] = 0.43529+/-0.0801 = (0.355186,0.51539)

Re-writing into ten-thousandths decimal places:
True proportion = (0.3552,0.5154)