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Constructing a Confidence Interval for a Population Proportion

Example:  In a poll conducted May 7-10, 2000, by ABC News, a simple random sample of 1068 American adults was asked, “Have you ever been shot at?”  Of the 1068 adults, 96 responded yes.  Obtain a 95% confidence interval about the population proportion, p.In this example, 1068 Americans are asked the question:  “Have you ever been shot at?”  96 individuals responded ‘Yes.’  Construct a 95% confidence interval for p, the true proportion of all Americans who have been shot at.

Press STAT, highlight TESTS, scroll through the options and select A:1-PropZInt.  The value for X is the number of Americans in the group of 1068 who have been shot at, so X = 96.  The number who were surveyed is n, so n = 1068.  Enter .95 for C-level.

Highlight Calculate and press ENTER.

In the output display the confidence interval for p is (.07273, .10704).  The sample proportion,    , is .08989 and the number surveyed is 1068.

Note:  You should calculate .  This value must be greater than or equal to 10 in order to use this confidence interval procedure.  (It is actually easier to do this calculation after you have calculated the confidence interval because the calculator displays the value of      as part of the output).  For this example, the calculation is 1068*.09*.91.  This value is greater than 10, so this supports the use of confidence interval procedure.