Question: 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 have 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.
c. You are interested in knowing what proportion of days in typical years have rain or snow in the area where you live. For the months of January and February, you record whether there is rain or snow each day, and then you calculate the proportion.
d. A large company wants to determine what proportion of its employees are interested in on-site day care. The company asks a random sample of 100 employees and calculates the sample proportion who are interested.