# Hypothesis Test For a Population Proportion Using the Method of Rejection Regions

Instructions:

It is assumed that you have already read the relevant chapter in your textbook and attended lecture on this topic.  Otherwise you will find this applet too challenging.  The purpose of this applet is to provide the student with guided practice through problems on hypothesis testing for a population proportion using the method of rejection regions.

1. Follow the instructions and hit the "Enter" key when you have finished entering in your step, or select the correct entry.

2. If you need a hint, click on the "Hint" Button".

3. Carry your calculations to three decimal places.  Use your three decimal places result for p^ when calculating the Z-score.

In the applet, the number of successes is labeled "r", so that p^ = r/n.

You will need the following table of z-critical values for this applet.

 a = 0.01 a = 0.05 a = 0.10 Z-Critical Value for a Left Tailed Test -2.33 -1.645 -1.28 Z-Critical Value for a Right Tailed Test 2.33 1.645 1.28 Z-Critical Value for a Two Tailed Test 2.58 1.96 1.645

Notice that two decimal places are given for some values while three are given for others.  The applet will accept 1.645 or the rounded 1.65.

Note:  For all of the examples given in this activity, the conditions np > 5 and nq > 5 are met.  This allows us to use the normal distribution to approximate the binomial distribution and proceed as the applet shows.  If the conditions had not been met, the normal distribution cannot be used.  A larger sample sized should be obtained.  Do not conduct a hypothesis test for a population proportion when the sample size is too small.

Note:  There are two common methods to conduct a hypothesis test.  This activity allows you to practice the method of rejection regions.  The other method involves the method of p-values.  For an applet on the P-Value method, click here.  Both methods are important to understand and both will always produce the same results.

Written Exercises

When you have mastered the above tutorial, please answer the following in a few complete sentences

1. Describe the steps in conducting a hypothesis test for a proportion?

2. Explain how conducting a hypothesis test for a proportion differs from conducting a hypothesis test for a mean.

3. Explain how the method of Rejection Regions differs from the method of P-Values.

Statistics Lecture Notes

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