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Side Effects of Prevnar – Hypothesis Test for a Proportion

Example:  The drug Prevnar is a vaccine meant to prevent meningitis.  (It also helps control ear infections.)  It is typically administered to infants.  In clinical trials, the vaccine was administered to 710 randomly sampled infants between 12 and 15 months of age.  Of the 710 infants, 121 experienced a decrease in appetite.  Is there significant evidence to conclude that the proportion of infants who receive Prevnar and experience a decrease in appetite is different from 0.135, the proportion of children who experience a decrease in appetite in competing medications?  Test using the P-value approach at the  level of significance.

This hypothesis test is a two-tailed test of:   vs.  .  The procedure that is used for this test is the 1-Proportion Test.  This test has two requirements.  The first requirement is:    To verify this, calculate 710*.135*(1-.135).   The result is greater than 10, so the first requirement is satisfied.  The second requirement is that the sample size is not more than 5% of the population size.  In this example, the population is all babies between 12 and 15 months of age.  We don’t know the exact size of the population, but it is in the millions.  The sample size of 710 is definitely less than 5% of the population size.

To run the test, press STAT, highlight TESTS and select 5:1-PropZtest.  This test requires a value for , which is the value of p in the null hypothesis.  Enter .135 for .  Next, a value for X is required.  X is the number of “successes” in the sample.  In this example, a success is “experiencing a decrease in appetite”, so X is equal to 121.  Next, enter the value for n.  Select for the alternative hypothesis and press ENTER.

Highlight Calculate and press ENTER.

The output displays the alternate hypothesis that was selected, the calculated Z-value, the P-value, the sample proportion,   , and the sample size.  (Note:     =121/710.)

Or, highlight Draw and press ENTER.

Since the P-value is less than a, the correct conclusion is to Reject .