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Suppose you work for a pharmaceutical company that is testing a new drug to treat ulcerative colitis. You conduct a random sample of 32 patients on the new drug and 14 of them indicated a decrease in symptoms since starting the drug regimen. You construct a 99% confidence interval for this proportion to be ( 0.2112 , 0.6638 ). What is the correct interpretation of this confidence interval?

1) We are 99% confident that the proportion of patients surveyed that have experienced a reduction in symptoms is between 0.2112 and 0.6638.

2) We are certain that 99% of patients will be between 0.2112 and 0.6638.

3) We cannot determine the proper interpretation of this interval.

4) We are 99% confident that the proportion of all patients on the drug regimen that have experienced a reduction in symptoms is between 0.2112 and 0.6638.

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