Listed below are the 35 members of the Metro Toledo...

Listed below are the 35 members of the Metro Toledo Automobile Dealers Association. We would like to estimate the mean revenue from dealer service departments. a. We want to select a random sample of five dealers. The random numbers are: $05,20,59,$ $21,31,28,49,38,66,08,29,$ and $02 .$ Which dealers would be included in the sample? b. Use the table of random numbers to select your own sample of five dealers. c. Use statistical software to select a simple random sample of five dealers. You must.enter the ID numbers $(00$ through 34$) .$ See page 243 for instructions. d. A sample is to consist of every seventh dealer. The number 04 is selected as the startinq point. Which dealers are included in the sample?

Listed below are the 35 members of the Metro Toledo Automobile Dealers Association. We would like to estimate the mean revenue from dealer service departments.
a. We want to select a random sample of five dealers. The random numbers are: $05,20,59,$ $21,31,28,49,38,66,08,29,$ and $02 .$ Which dealers would be included in the sample?
b. Use the table of random numbers to select your own sample of five dealers.
c. Use statistical software to select a simple random sample of five dealers. You must.enter the ID numbers $(00$ through 34$) .$ See page 243 for instructions.
d. A sample is to consist of every seventh dealer. The number 04 is selected as the startinq point. Which dealers are included in the sample?

Key Concepts

Sampling Frame

A sampling frame is the complete list of all the elements in the population from which a sample is to be drawn. In this case, the list of 35 dealers is the sampling frame. Having a well-defined sampling frame is essential to ensure that every member of the population has a known chance of being included in the sample.

Simple Random Sampling

Simple random sampling is a method in which each member of the population has an equal chance of being selected in the sample. This method eliminates bias and ensures that the sample is representative of the population, which is fundamental for accurate statistical inference about the mean revenue.

Random Number Tables

Random number tables are tools used to select a simple random sample from a population. These tables are lists of numbers generated by a random process, and by following specific rules (like identifying valid numbers that fall within the range of the sampling frame), they help in systematically drawing random samples without bias.

Systematic Sampling

Systematic sampling involves selecting elements from the sampling frame using a fixed, periodic interval, known as the sampling interval. After randomly selecting a starting point, every kth element is chosen. This method provides a simple and efficient way of performing sampling while still attempting to maintain randomness.

Statistical Software for Sampling

Statistical software is frequently used to perform random sampling, and it can automate the process of selecting a simple random sample. By enabling precise and reproducible selection criteria, such software reduces human error and further ensures that the sample is representative of the broader population.

Transcript

00:01 All right, so we've got 35 members of the automobile dealers association.

00:08 We're trying to estimate the mean revenue for the dealer service departments.

00:14 And the one selected are numbered zero to 34, 35 in total.

00:19 And just if we selected, we went five dealers and random numbers were selected.

00:24 And we don't know which dealers would be included in the sample.

00:27 So we've got the fifth one.

00:29 So we've got bob schmidt.

00:30 Just read off the number 20 great lakes 59 that there isn't the 59th one the 21st one grogantown 31 that's going to be there south side and we only want five and then 28 okay so i think that's five one two three four and five yep there we go so we got bob smit great lakes grogan ruin and south side so there you go the other ones would be included because we've already got, even though there is a 29th one and a second one and an eighth one, we wouldn't select them because we've already selected our five.

01:15 So there you go.

01:22 Use a random table of random numbers to select your own sample.

01:27 This could be anything, whatever you want to do.

01:29 I mean, this is, let your creative juices flow here, people.

01:35 So let's see, we're going to do, it's 849 right now, 849 by my clock.

01:44 So i'm going to say looking at the eighth row, well, starting with the ninth one, we're going to count every four.

02:00 That's how i'm going to do this.

02:01 So starting with the eighth row, one, two, three, four, five, six, seven, eight.

02:05 Starting on the ninth one, we're going to count every four.

02:09 One, two, three, four, five, six, and eight, nine.

02:13 So that's the first one, and we're going to count every four.

02:15 One, two, three, four.