You want to ask a sample of high school students the...

You want to ask a sample of high school students the question “How much do you trust information about health that you find on the Internet—a great deal, somewhat, not much, or not at all?” You try out this and other questions on a pilot group of 5 students chosen from your class. The class members are listed at top right. (a) Explain how you would use a line of Table D to choose an SRS of 5 students from the following list. Explain your method clearly enough for a classmate to obtain your results. (b) Use line 107 to select the sample. Show how you use each of the digits. Anderson Deng Glaus Nguyen Samuels Arroyo De Ramos Helling Palmiero Shen Batista Drasin Husain Percival Tse Bell Eckstein Johnson Prince Velasco Burke Fernandez Kim Puri Wallace Cabrera Fullmer Molina Richards Washburn Calloway Gandhi Morgan Rider Zabidi Delluci Garcia Murphy Rodriguez Zhao

You want to ask a sample of high school students the question “How much do you trust information about health that you find on the Internet—a great deal, somewhat, not much, or not at all?” You try out this and other questions on a pilot group of 5 students chosen from your class. The class members are listed at top right.

(a) Explain how you would use a line of Table D to choose an SRS of 5 students from the following list. Explain your method clearly enough for a classmate to obtain your results.
(b) Use line 107 to select the sample. Show how you use each of the digits.

Anderson Deng Glaus Nguyen Samuels
Arroyo De Ramos Helling Palmiero Shen
Batista Drasin Husain Percival Tse
Bell Eckstein Johnson Prince Velasco
Burke Fernandez Kim Puri Wallace
Cabrera Fullmer Molina Richards Washburn
Calloway Gandhi Morgan Rider Zabidi
Delluci Garcia Murphy Rodriguez Zhao

Key Concepts

Simple Random Sampling

Simple random sampling (SRS) is a method where each member of the population has an equal chance of being selected. In this approach, every individual is assigned a unique identifier, and selections are made solely by random mechanisms, ensuring the sample is unbiased and representative of the population.

Random Digit Table

A random digit table is a prearranged grid of digits that are generated in a random order. Researchers use these tables to make selections by choosing a starting point and reading consecutive digits in a specified direction (for example, left-to-right), ensuring that the sample is drawn in a randomized manner.

Listing and Numbering the Sampling Frame

Before using the random digit table, it is important to create a complete list (sampling frame) of all individuals in the population and assign each a unique number. This numbering allows the researcher to match groups of digits from the random digit table with specific individuals in the list.

Procedure for Using a Random Digit Table

The procedure typically involves selecting a random starting point within the random digit table and reading off groups of digits that correspond to the assigned numbers in the sampling frame. Any group of digits that falls outside the range of assigned numbers is skipped, and the process continues until the required sample size is reached.

Transcript

00:01 In question number 11, we're given a situation where we have to sample high school students, and we have a total of 40 students, and we want to use table d in our textbook to choose five different students to sample.

00:19 Well, we're asked to explain clearly the method that we would use to use their table of random digits to select those five students.

00:29 So whenever you're asked to explain how to use the table of random digits, you need to be so detailed that whoever can read your writing can copy your method and get the exact same results.

00:41 So here we go.

00:49 All right, since there are 40 students, we're going to assign each student a number between 0 -1 and 40.

00:56 Now, it's important here that we assign each student a two -digit number because there's 40 total students, 40 being a two -digit number.

01:03 We should also treat the single -digit values 1 through 9, or i'm sorry, zero -through -9 actually, as two -digit numbers.

01:09 Now you can start at 0 -0, if you would like.

01:12 Can go through 39, you can start at 0 1 and go through 40.

01:15 Either one is okay as long as you have 40 values that you can choose from.

01:20 Then we're going to be detailed here saying moving left to right on table d, look at each two -digit value.

01:27 If the value is within the range of 0 -1 to 40, we're going to select the number and continue until four other values between 0 -1 and 40 are selected.

01:38 This also brings up the idea of repeated values and any other numbers that aren't in our range.

01:43 To mention what we're going to do with those values.

01:45 So i'm going to say skip repeated numbers, which means we're sampling without replacement.

01:52 We're also going to skip zero zero because we're not including that one.

01:55 41 through 99.

01:57 This is going to take care of any two -digit number that's not in our range.

02:02 When five numbers are selected, figure out which students were assigned those numbers in order to create the sample.

02:12 In part b, we're asked to use line 107 on table d, which is the table of random digits to select the sample.

02:20 And we're given the list of students in our textbook.

02:22 We're going to label those students 0 -1 through 40, just like the instructions above say.

02:27 And they're labeled, they're listed alphabetically.

02:30 So we're going to number them also alphabetically.

02:32 So i'm sorry, numerically.

02:34 So the very first student alphabetically is going to be the very first student numerically.

02:38 And that's how we're going to label it.

02:42 So i've recorded the random numbers that we're in table d here...

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