# Hypothesis Testing: Two sample Z test for proportion

1.To compare the effectiveness of two treatments 1 and 2 for a particular disease. Patients were separated in 2 treatment groups. A patient in group 1 received treatment 1 and patients in group 2 received treatment 2. The results are given in the table below:

Treatment 1 Treatment 2

Success 170 180

Failure 30 10

(a) To answer the following question "Do treatments 1 and 2 have different effectiveness?", which test statistic should we use?

(b) A student, to whom the problem had been submitted, replied affirmatively to the question asked. Is the answer correct?

https://brainmass.com/statistics/z-test/hypothesis-testing-two-sample-test-proportion-328207

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Test statistic

1. To compare the effectiveness of two treatments 1 and 2 for a particular disease. Patients were separated in 2 treatment groups. A patient in group 1 received treatment 1 and patients in group 2 received treatment 2. The results are given in the table below:

Treatment 1 Treatment 2

Success 170 180

Failure 30 10

(a) To answer the following question "Do treatments 1 and 2 have different effectiveness?" which test statistic should we use?

Answer

The Test Statistic we should use is

where

Here x1 = 170, x2 = 180, n1 = 170 + 30 = 200, n2 = 180 + 10 = 190.

p1 = ...

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.