A very large school system claims that it has a 85% graduation rate. A sample of 900 seniors found that 725 received their high school diploma.

1.    A very large school system claims that it has a 85% graduation rate. A sample of 900 seniors found that 725 received their high school diploma. Construct a 90% proportion confidence interval based on this data and determine whether the data supports the 85% statement.

Start by using the binomial distribution.  = n    σ =

a.     What is n? 

b.   What is ? 

c.   What is ?

d.   What is ?

e.     What is p? (Note: p is based on our belief about the population. is based on the sample.)

f.      What is σ? 

g.     Let  σp = sqrt(). What is σp ? 

h.    We want to make a 90% confidence interval by using the formula

z = k/σp

Should we use a 1 tail or 2 tail z-score?

i.      What value of z corresponds to the desired 90% confidence interval? 

j.      What is k? 

k.    Construct the confidence interval

( - k) < ptrue < ( + k)

l.      Is your confidence intervalconsistent with the belief that 85% of high school students graduate? (yes or no, and explain your answer using your computed confidence interval).