Please show calculations and formulas used to work this problem.
A study of motel facilities in Rock Hill, South Carolina, showed there were 25 facilities. The city's convention and visitors bureau is studying the number of rooms at each location. The results are as follows
90 72 75 60 75 72 84 72 88 74 105 115 68 74 80 64 104 82 48 58 60 80 48 58 100
a. Using a table of random numbers (Appendix E), select a random sample of five motels from this population.
b. Obtain a systematic sample by selecting a random starting point among the first five motels and then select every fifth motel.
c. Suppose the last five motels are "cut-rate" motels. Describe how you would select a random sample of three regular motels and two cut-rate motels.
A recent study by the Greater Los Angeles Taxi Drivers Association showed that the mean fare charged for service from Hermosa Beach to the Los Angeles International Airport is $18.00 and the standard deviation is $3.50. We select a sample of 15 fares.
a. What is the likelihood that the sample mean is between $17.00 and $20.00?
b. What must you assume to make the above calculation?
This solution shows how to obtain a random and systematic sample and also finds the likelihood of the sample mean being a specific number. All steps are shown with brief explanations.