Question

For Exercises explain how each experiment can be simulated by using random numbers.

Almost 16% of Texas residents are foreign-born. Explain how to select a sample of 40 based on this scenario.

Answer 1

It is stated that almost 16% of Texas residents are foreign-born. We need to select a sample of 40 basing on simulation using random numbers.

 

Step 1: We first list the possible outcomes.

The residents of Texas can be divided into two categories based on our study. They are Texas-born or foreign-born.

 

Step 2: Assign the probabilities to each outcome.

It is given that 16% of Texas residents are foreign-born. Therefore,

P(foreign-born) = 0.16, P(Texas-born) = 0.84.

 

Step 3: Set up a correspondence between the random numbers and the outcome.

Use random numbers 001 to 016 to represent foreign-born residents and 017 to 100 to represent Texas-born residents.

 

Step 4: Select random number from table and categorize based on the classification given in the previous step. That is, if the random number is between1-16, then we consider that a foreign-born resident is included in the sample, otherwise, we can consider that a Texas-born resident is included in the sample.

 

Step 5: Continuing the procedure, we can select 40 residents into sample.