Explain whether each of the following situations meets the conditions for which the Rule for Sample Proportions applies. If not, explain which condition is violated.
a. Unknown to the government, 10% of all cars in a certain city do not meet appropriate emissions standards. The government wants to estimate that percentage, so they take a random sample of 30 cars and compute the sample proportion that do not meet the standards.
b. The Census Bureau would like to estimate what proportion of households has some­one at home between 7 p.m. and 7: 30 p.m. on weeknights, to determine whether that would be an efficient time to collect census data. The Bureau surveys a random sample of 2000 households and visits them during that time to see whether someone is at home.