The American Society for Microbiology (ASM) and the Soap and Detergent Association (SDA) jointly commissioned two separate studies, both of which were conducted by Harris Interactive. In one of the studies, 1001 adults were interviewed by telephone and asked about their handwashing habits. In the telephone interviews, 921 of the adults said they always wash their hands in public restrooms. In the other study, the hand-washing behavior of 6076 adults was inconspicuously observed within public restrooms in four U.S. cities and 4679 of the 6076 adults were observed washing their hands. a. In the telephone survey, what is the variable of interest? Is it qualitative or quantitative? b. What is the sample in the telephone survery? What is the population to which this study applies? c. Verify that the requirements for constructing a confidence interval for the population proportion of adults who say they always wash their hands in public restrooms are satisified. d. Using the results from the telephone interviews, construct a 95% confidence interval for the proportion of adults who say they always was their hands in public restrooms. e. In the study where hand-washing behavior was observed, what is the variable of interest? Is it qualitative or quantitative? f. We are told that 6076 adults were inconspicuously ob served, but wer are not told how these adults were selected. We know randomness is a key ingredient in statistical studies that allows us to generalize results from a sample to a population. Suggest some ways randomness might have been used to select individuals in this study. g. Verify the requirements for constructing a confidence interval for the population proportion of adults who actually washed their hands while in a public restroom. h. Using the results from the observational study, construct a 95% confidence interval for the proportion of adults who wash their hands in public restrooms. 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? j. Cite some sources of variability in both studies. k. You wish to conduct your own telephone survey to determine the proportion of adults in the US who always wash their hands in public restrooms. What sample size would be needed for the estimate to be within 3 percentage points with 95% confidence if you use the estimate obtained in part (a). What sample size would be needed if you do not have a prior estimate?