Find the test statistic and the p-value.

Question

Independent random samples, each containing 70 observations, were selected from two populations. The samples from populations 1 and 2 produced 59 and 49 successes, respectively.
Test H0:(p1−p2)=0 against Ha:(p1−p2)≠0. Use α=0.08.

(a) The test statistic is ?

(b) The P-value is ?

Answer 1

Test statistic is

 

Z = 2.013 = (p1-p2)/standard error where p1 = 59/70, p2 = 49/70 and standard error = .070978

 

A Z score of 2.013 gives us a p value of .044 which is less than .08, therefore the two proportions are statistically different from each other.

Answer 2

 p1 = 59/70 

 p2 = 49/70

 

 

 the error margin is:

    sqrt (  pi * (1-p1) / 70) + p2(1-p2)/70) =

   sqrt (   59/70 * 11/70 + 49/70 * 21/70  ) =

  sqrt (  (  59*11 + 49*21)/4900  ) = 0.5852

 

The difference p1 - p2 = 10/70 = 1/7

the p -value is 1.75 per the normal distribution table.

 

1.75 * 0.5852 = 1.0241

 

1/7 + 1.0241 = 1.16

 

Accept Null hypothesis.... no difference in proportions