Question

A random sample of 80 mizzou students showed that 44 had driven a car during the day before the survey was conducted. suppose that we are interested in forming a 80 percent confidence interval for the proportion of all mizzou students who drove a car the day before the survey was conducted.

Answer 1

You are asked:
a) the estimate
b) the standard error
c) the multiplier

A) The point estimate is given by:
p = sample size / population size
   = 44/80
   = 0.55

B) The standard error is given by:
SE = $\sqrt{ \frac{p(1-p)}{n} }$
     = $\sqrt{ \frac{0.55(1-0.55)}{80} }$
     = 0.0556

C) In order to find the multiplier (z-score), you first need to calculate the probability:
(1-0.80)/2 = 0.10
Now, look at a z-table to find z = 2.32