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Problem 38 Hard Difficulty

Bob Miller, a food critic, wants to prepare an article on the quality of food at locally owned restaurants in Myrtle Beach, South Carolina. A list of 44 locally owned restaurants is contained in the data file named Dining that is on the website that accompanies this text (Coastal Carolina Dining, Fall $2004 ) .$ Bob only has time to sample the food at 5 of these restaurants.
a. In the data file the restaurants are listed in column $A$ of an Excel worksheet. In column $B$ we generated a random number for each of the restaurants in column A. Use these random numbers to select a simple random sample of five restaurants for Bob.
b. Generate a new set of random numbers and use them to select a new simple random sample. Did you select the same restaurants?

Answer

a. Thoroughbreds, The Marker, Officers Club, SeaBlue, Crickets
b. Generate 44 random numbers between 0 and 1, each random number corresponds with one restaurant in the list. The sample contains the restaurants corresponding to the 5 smallest random numbers.

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Video Transcript

All right. So this question gives us a list of 44 restaurants in their associative random numbers, and it wants us toe list the five that would be in the sample. So the fine of that would be in the sample are those with the lowest numbers. So if we look through are five lowest numbers belong to the following restaurants. The 1st 1 iss thorough reds. The second is the marker with the third his officers club the fourth, the sea blue and last but not least, his crickets. And these what? The five with smallest random numbers. Now, Part B wants us to make a simple by generating random numbers and see if we get the same result. So I'll just outlined the procedure. First thing we d'oh number the restaurants from one so 44 them generate a random number for each and then three pick the five smallest numbers. Okay, and then it asks if we'll get the same sample. Is he does? Probably not, because there are. They're 44. Choose five possible samples. So the probability of receiving the same execs sample as the guy and the question that is very slip it is possible and it's non zero. But it's just unlikely we'll probably get a totally different sample using this procedure here because we'll get totally.