Question No 4 [3 + 3) a) In a random sample of 1000 families owning television sets in the city of Hamilton, Canada, it is found that 0.62 subscribe to HBO. Find a 95% confidence interval for the actual proportion of families with television sets in this city that subscribe to HBO. b) A study was conducted in which two types of engines, A and B. were compared. Gas mileage, in miles per gallon, was measured. Fourty five experiments were conducted using engine type A and Fifty experiments were done with engine type B. The gasoline used and other conditions were held constant. The average gas mileage was 20 miles per gallon for engine A and 24 miles per gallon for engine B. Find a 90% confidence interval on Ma-He, where and Me are population mean gas mileages for engines A and B, respectively. Assume that the population standard deviations are 3 and 5 for engines A and B, respectively