6. (2+2=4 marks) In a random sample of 1000 homes in a certain town, 228 homes were found to be heated by oil. a. Find 99% confident interval for the proportion of the homes in the town that are heated by oil Keep three digits after decimal point in the answer a. 99% confidence interval for the proportion of the homes in the town that are heated by oil is Show your work in finding 99% confidence interval for the population proportion. b. At least how many homes should be included into the sample if we want to be 99 % confident that the sample proportion will be within 0.05 of the population proportion of homes in the town that are heated by oil? The minimum number of homes that should be included into the sample is Show your work in finding the minimum number of homes that should be included into the sample.