Question

The manager of a myrtle beach hotel chain wants to give a survey to customers for customer satisfaction after their stay at the hotel. Half of the rooms are located on the front part of the hotel facing the beach, and the other half of the rooms are on the back side of the hotel facing the street. There are two different towers, one in north myrtle beach and one in south myrtle beach. Each tower holds 400 rooms, with 20 on each floor. Explain how to select a simple random sample of 80 rooms. Explain how to select a stratified random sample of 80 rooms. Explain why selecting 4 of 40 different floors would not be a good way to obtain a cluster sample?

Answer 1

To select a simple random sample of 80 rooms, assign a number to each room and use a random number generator. To select a stratified random sample, divide the hotel based on room location and towers. Selecting 4 of 40 floors would not be a good cluster sample.

Step-by-step explanation:

To select a simple random sample of 80 rooms from the hotel, you can assign a number to each room and then use a random number generator to select the 80 rooms. For example, if the hotel has 800 rooms, you can assign each room a number from 1 to 800, and then use a random number generator to generate 80 unique numbers between 1 and 800. These 80 rooms will form your simple random sample.

To select a stratified random sample of 80 rooms, you can divide the hotel into two strata based on room location (front facing the beach and back facing the street) and two more strata based on towers (north Myrtle Beach and south Myrtle Beach). Within each stratum, you can randomly select rooms proportionally based on the number of rooms in each stratum. For example, if there are 400 rooms in each tower, you can randomly select 40 rooms from each tower, which will give you a total of 80 rooms in your stratified random sample.

Selecting 4 of 40 different floors would not be a good way to obtain a cluster sample because the variability of the rooms within each floor could be very different. For example, one floor may have mostly suites, while another floor may have mostly single rooms. By selecting only a few floors, you may not capture the true variability of the entire hotel.