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 one of the studies, 1001 adults were interviewed by telephone and asked about their hand-washing habits. In the other study, the hand-washing behavior of 6076 adults was inconspicuously observed within public restrooms in four U.S. cities. Address the following: a. In the telephone interviews, 921 of the adults said they always wash their hands in public restrooms. Use this result to obtain a point estimate for the proportion of adults who say they always wash their hands in public restrooms. b. Verify that the requirements for constructing a confidence interval for p from part (a) are satisfied. c. Using the results from the telephone interviews, construct and interpret a 95% confidence interval for the proportion of adults who say they always wash their hands in public restrooms. d. Is it possible that the proportion of adults who say they always wash their hands in public restrooms is less than 0.85? Is this likely? e. In the observational study, 4679 of the 6076 adults were observed washing their hands. Use this result to obtain a point estimate for the proportion of adults who wash their hands in public restrooms. f. Verify that the requirements for constructing a confidence interval for p from part (e) are satisfied. g. Using the results from the observational study, construct and interpret a 95% confidence interval for the proportion of adults who wash their hands in public restrooms. h. Is it possible that the proportion of adults who wash their hands in public restrooms is greater than 0.85? Is this likely? i. Based on your findings in parts (a) through (h), what might you conclude about the proportion of adults who say they always wash their hands versus the proportion of adults who actually wash their hands in public restrooms? Why do you think this is?
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 one of the studies, 1001 adults were interviewed by telephone and asked about their hand-washing habits. In the other study, the hand-washing behavior of 6076 adults was inconspicuously observed within public restrooms in four U.S. cities. Address the following: a. In the telephone interviews, 921 of the adults said they always wash their hands in public restrooms. Use this result to obtain a point estimate for the proportion of adults who say they always wash their hands in public restrooms. b. Verify that the requirements for constructing a confidence interval for p from part (a) are satisfied. c. Using the results from the telephone interviews, construct and interpret a 95% confidence interval for the proportion of adults who say they always wash their hands in public restrooms. d. Is it possible that the proportion of adults who say they always wash their hands in public restrooms is less than 0.85? Is this likely? e. In the observational study, 4679 of the 6076 adults were observed washing their hands. Use this result to obtain a point estimate for the proportion of adults who wash their hands in public restrooms. f. Verify that the requirements for constructing a confidence interval for p from part (e) are satisfied. g. Using the results from the observational study, construct and interpret a 95% confidence interval for the proportion of adults who wash their hands in public restrooms. h. Is it possible that the proportion of adults who wash their hands in public restrooms is greater than 0.85? Is this likely? i. Based on your findings in parts (a) through (h), what might you conclude about the proportion of adults who say they always wash their hands versus the proportion of adults who actually wash their hands in public restrooms? Why do you think this is?
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