A reporter for Time Magazine was interested in residents’ levels of worry about being the victim of crime in their neighborhood. They performed a telephone poll of 500 adult Americans, 140 from urban areas, 160 from suburban, and 200 from rural areas. The number of adults who reported worring about being a victim of crime was urban:83, suburban: 92, and rural: 86. (a) Perform a hypothesis test at the 5% level of significance to determine if there is evidence of a difference in the proportion of urban and suburban residents who worry about being the vicim of crime? (Be sure to state your hypotheses, assumptions, and show your computations.)
(b) Create a 95% confidence interval for the difference in proportion of rural and urban residents who worry about being a victim of crime.(Be sure to state your assumptions and show your computations.)

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i. e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)