Islands of Adventure contains the Wizarding World of Harry Potter - Hogsmeade, w

Question

Islands of Adventure contains the Wizarding World of Harry Potter - Hogsmeade, which features Harry Potter and the Forbidden Journey. In this attraction, you make your way through familiar classrooms and corridors of Hogwarts School of Witchcraft and Wizardry, then you soar above the castle grounds as you join Harry Potter and his friends on an unforgettably thrilling adventure, coming face-to-face with magical creatures. Of interest is to determine the average wait time for all guests on the Harry Potter and the Forbidden Journey attraction during June 2015. Guests with a two-park admission ticket can ride the Hogwarts Express to travel from one park to the other. From the train windows, guests see some of the magnificent scenery of London and the British countryside, and encounter characters featured in the films as they travel between London and Hogsmeade. Suppose that on one train there are 354 guests, and the goal is to select a simple random sample of 8 such guests to provide feedback on the experience. Explain in detail what you would do to select a simple random sample of 8 of these guests, and give the numbers of the 8 guests that you would have chosen. The list of numbers below is a row of random digits from a random number table and please start at the far left of that row. Use the procedure illustrated in class. 20194411459035822957232850920854829109485767859105938502948503958239447728298347103494735599

Explanation / Answer

We needto select a simple random sample of size 8 from a population of 354 using the given row from a random number table. We will do this as explained in detail below.

1. Let us first number the passengers of the train serially from 1 to 354.

2. Next let us split the given random number row into groups of 3 digit numbers as given below:

201 944 114 590 358 229 572 328 509 208 548 291 094 857 678 591 059 385 029 485 039 582 394 477 282 983 471 034 947 355 99

3. Next let us check each of the above 3-digit random numbers whether it is <= 354. If yes, then we will select the passenger with that serial no. If not, we will skip that number and go to the next random number in the list.

4. Thus the first number is 201, which is < 354. Hence passenger no 354 is selected for the sample. Next number is 944 which is >354, hence skip it and go to next number 114 which is <= 354 and hence selected.

5. Following this process, we get the sample given below:

201, 114, 229, 328, 208, 291, 94, 59

The above set of 8 serial numbers is the simple random sample required for the survey.

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