A hotel maintenance crew wants to estimate how many of the 12,000 lamps in their 30-story hotel need a new light bulb. Which of the following is a random sample of lamps to be inspected?
a all lamps from the rooms with king-sized beds
b all lamps in booked rooms
c 100 lamps on each floor chosen randomly
d 400 lamps on the first 10 floors
c 100 lamps on each floor chosen randomly.
Is it c because it is the only one chosen randomly?
Yes, that is correct. Option c is the only one that involves random selection. The other options select lamps based on certain criteria (e.g. all lamps from rooms with king-sized beds or all lamps in booked rooms), which may not be representative of the entire population of lamps in the hotel.
The correct answer is c: 100 lamps on each floor chosen randomly.
When conducting a random sample, it is important to ensure that the sample is representative of the whole population. In this case, the population is the 12,000 lamps in the 30-story hotel.
Option a, inspecting all lamps from rooms with king-sized beds, does not provide a random sample because it only includes a specific subset of lamps. This may introduce bias in the sample.
Option b, inspecting all lamps in booked rooms, also does not provide a random sample as it only includes lamps in rooms that are currently occupied. This may not represent the overall condition of all lamps in the hotel.
Option d, inspecting 400 lamps on the first 10 floors, does not provide a random sample either. It is specific to the first 10 floors and the number of lamps chosen is not proportional to the total number of lamps in the hotel.
Option c, inspecting 100 lamps on each floor chosen randomly, is the best option to obtain a random sample. This method ensures that lamps from each floor are included in the sample and the number of lamps chosen is proportionate to the total number of lamps in the hotel.