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Find the test statistic and the p-value.

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 ?

2 Answers by Expert Tutors

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Walter B. | Success-Based Tutor Specializing in Your StudentSuccess-Based Tutor Specializing in Your...
4.9 4.9 (532 lesson ratings) (532)
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.
Andy C. | Math/Physics TutorMath/Physics Tutor
4.9 4.9 (19 lesson ratings) (19)
1
 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
 
 
 
 

Comments

Andy, take a look at your formula for the standard error. It is not correct. Check your formula.
Andy, check your math for that Z test of two proportions. You used the wrong formula for the standard error. The Z value should be 2.013 and a p value of .044. 
Andy,
 
Not quite sure where you went wrong, but it looks like you need to recalculate the denominator of your test statistic. As you remember, the appropriate test statistic is a z test with the difference in proportions as the numerator and the standard error of the two proportions as the  numerator. I am happy to send you the formula for the standard error of two proportions.