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\fDuring 2008, 3.0% of all U.S. households were burglary victims. For a simple random sample of 300 households from a certain region, suppose that 18 households were victimized by burglary during that year. Apply an appropriate hypothesis test and the 0.05 level of significance in determining whether the region should be considered as having a burglary problem greater than that for the nation as a whole.A 1931 issue of Time magazine contained an advertisement for Liberty magazine. According to a study cited by Liberty, it was found that 15% of Liberty families had a "mechanical refrigerator," compared to just 8%% for all U.S. families. Assuming that the study included a sample of 120 Liberty families, and using the 0.01 level of significance, could the percentage of Liberty families owning this modern (for 1931) convenience be higher than for the nation overall?The administrator of a local hospital has told the governing board that 30% of its emergency room patients are not really in need of emergency treatment (i.e., the problems could just as easily have been handled by an appointment with their family physician). In checking a random sample of 400 emergency room patients, a board member finds that 35%% of those treated were not true emergency cases. Using an appropriate hypothesis test and the 0.05 level, evaluate the administrator's statement.\fBefore accepting a large shipment of bolts, the director of an elevator construction project checks the tensile strength of a simple random sample consisting of 20 bolts. She is concerned that the bolts may be counterfeits, which bear the proper markings for this grade of bolt, but are made from inferior materials. For this application, the genuine bolts are known to have a tensile strength that is normally distributed with a mean of 1400 pounds and a standard deviation of 30 pounds. The mean tensile strength for the bolts tested is 1385 pounds. Formulate and carry out a hypothesis test to examine the possibility that the bolts in the shipment might not be genuine.The average U.S. household has $235,800 in life insurance. A local insurance agent would like to see how households in his city compare to the national average, and selects a simple random sample of 30 households from the city. For households in the sample, the average amount of life insurance is w. = $245,800, with s = $25,500. Source: reuters.com, September 23, 2008. a. Using a nondirectional hypothesis test and a level of significance of your choice, what conclusion would be reached? b. For the significance level used in part (a), construct the appropriate confidence interval and verify the conclusion reached in part (a)