In the second study, the hand-washing behavior of a sample of 6,067 adults was inconspicuously observed in public restrooms in several U.S. cities. In this study, 4,679 of those adults were observed washing their hands, while the rest did not.

Based on the results of the second study, determine a 90% confidence interval for the proportion of adults who actually wash their hands in public restrooms.

1. The American Society for Microbiology (ASM) and the Soap and Detergent Association (SDA) jointly commissioned two separate studies during 2007, both of which were conducted by Harris Interactive. In the first study, a sample of 1,001 adults were interviewed by telephone and asked about their hand- washing habits. In that sample, 921 of the adults said they always wash their hands in public rest rooms. a. (3) Based on the results of the first study, determine a 90% confidence interval for the proportion of adults who say they always wash their hands in public rest rooms. In the second study, the hand-washing behavior of a sample of 6,067 adults was inconspicuously observed in public restrooms in several U.S. cities. In this study, 4,679 of those adults were observed washing their hands, while the rest did not. b. (3) Based on the results of the second study, determine a 90% confidence interval for the proportion of adults who actually wash their hands in public rest rooms. Based on the results of the two studies, you're going to test (at the 5% significance level) whether the proportion of adults who actually wash their hands in public rest rooms is less than the proportion of adults who say they wash their hands in public rest rooms