Enter x (# of successes) Enter n (sample size) Enter H0 Enter α
p
 
64 randomly selected items were tested. It was found that 56 of the items tested positive.
Test the hypothesis that exactly 80% of the items tested positive at α = 0.01

State the null and alternative hypothesis:

H0:  p = 0.8
HA:  p ≠ 0.8

Compute

p^  =  x
  n

p^  =  56
  64

p^ = 0.875

Calculate our test statistic z:

z  =  p^ - p
  √p(1 - p)/n

z  =  0.875 - 0.8
  √0.8(1 - 0.8)/64

z  =  0.075
  √0.8(0.2)/64

z  =  0.075
  √0.0025

z  =  0.075
  0.05

z = 1.5

Checking our table of z-scores for α = 0.01%, we get:

Z = 2.3263

Our rejection region is Z > 2.3263