There are 25 motels in Goshen, Indiana. The number of rooms in each motel follow
ID: 3250464 • Letter: T
Question
There are 25 motels in Goshen, Indiana. The number of rooms in each motel 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. Suppose we wish to obtain a systematic sample by selecting a random starting point among the first five motels and then select every fifth motel. If we select the third observation as starting point then the rest of the sample would include 75, . b. For a sample of 5 motels if the first motel chosen is the second one and every fourth is chosen give the numbers of the motels chosen. So the sample consists 72, . 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. Three can be chosen from the first 20 motels in ways. Two can be chosen from the last 5 motels in ways. Totally there can be possible samples.
Explanation / Answer
a) There can be a total of 5 ways since the only independent task is to select the first motel. The other 4 are decided automatically by adding 5 to the number selected.
b) The motels chosen will be the ones numbered 2,6,10,14,18,22 only. Hence, 6 motels will be chosen in all.
3) No of ways = Ways of chosing 3 regular motels from 20 ways * ways of choosing2 cut-rate motels from 5 ways Hence, total no. of ways = 20C3 * 5C2 = 20*19*18/6* 5*4/2 = 11400 ways
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