l Hypothesis Testing for a proportion Calculator
Enter x (# of successes) Enter n (sample size) Enter H0 Enter α
p
 
39 randomly selected items were tested. It was found that 9 of the items tested positive.
Test the hypothesis that no more than 50% of the items tested positive at α = 0.10

State the null and alternative hypothesis:

H0:  p < 0.5
HA:  p > 0.5

Compute

p^  =  x
  n

p^  =  9
  39

p^ = 0.23076923076923

Calculate our test statistic z:

z  =  p^ - p
  √p(1 - p)/n

z  =  0.23076923076923 - 0.5
  √0.5(1 - 0.5)/39

z  =  -0.26923076923077
  √0.5(0.5)/39

z  =  -0.26923076923077
  √0.0064102564102564

z  =  -0.26923076923077
  0.080064076902544

z = -3.3626912299068

Checking our table of z-scores for α = 0.10%, we get:

Z = 1.2816

Our rejection region is Z > 1.2816