Question

Do you trust the Internet? 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 the 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.

Short answer

Part (a) Make a list of two-digit numbers, skipping those that aren't between $01$ and $40$ or are repeats, until you have five distinct numbers between $01$and $40$

Part (b) Our SRS of $5$Pilot group of students chosen from class is:

Johnson$\left(20\right)$

Drasin $\left(11\right)$

Washburn $\left(38\right)$

Rider$\left(31\right)$and Calloway $\left(07\right)$

Step-by-step solution

Part (a) Step 1: Given information

The sample of $40$students is given

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

Part (a) Step 2: Concept

A simple random sample (SRS) of size is made up of $n$people chosen from the population with an equal chance of being the sample that is actually chosen.

Part (a) Step 3: Explanation

Each student should be alphabetized from $01$ to $40$ Pick a starting point from the random number table. Make a list of two-digit numbers, skipping those that aren't between $01$ and $40$ or are repeats, until you have five distinct numbers between $01$ and $40$

Part (b) Step 1: Explanation

The random digit table will be used to select an SRS in a two-step process.

1) Alphabetically label each student from $1$to $40$Labels $01$to $40$have been added to the alphabetized list of students in the table below:

2) Using the database of random digits Start reading two-digit groupings from the left side of line $107$Because our pupils are designated $01-40$select the first $5$unique numbers ranging from $01-40$which will be selected kids. Because the same student cannot be selected more than once, if the number is repeated, use it just once.

Here is the beginning of the line $107:$

Group the above digits to two digit numbers. We get:$82739578902080747511816765530094383148936094072024$

Our SRS of $5$pilot students was chosen from the class:$$\begin{gathered} 82,73,95,78,90,20,80,74,75,11,81,67, \\ 65,53,00,94,38,31,48,93,60,94,07,20,24 \end{gathered}$$

Johnson$\left(20\right)$

Drasin $\left(11\right)$

Washburn $\left(38\right)$

Rider $\left(31\right)$and Calloway $\left(07\right)$