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Ch 4.1 + 4.2 Sampling

Sampling with a Random Number Table

Random Number Tables – they are tables with randomly generated groups of numbers in

them.

How to use a random number table

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|Let's assume that we have a population of 185 students and each student has been | |

|assigned a number from 1 to 185. Suppose we wish to sample 5 students (although we | |

|would normally sample more, we will use 5 for this example). | |

|Since we have a population of 185 and 185 is a three digit number, we need to use the | |

|first three digits of the numbers listed on the chart. | |

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|We close our eyes and randomly point to a spot on the chart. For this example, we will assume that we selected 20631 in the first column. |

|We interpret that number as 206 (first three digits). Since we don't have a member of our population with that number, we go to the next number 899 (89990). |

|Once again we don't have someone with that number, so we continue at the top of the next column. As we work down the column, we find that the first number to|

|match our population is 100 (actually 10005 on the chart). Student number 100 would be in our sample. Continuing down the chart, we see that the other four |

|subjects in our sample would be students 049, 082, 153, and 005. |

|Del Siegle, Ph.D. Neag School of Education - University of Connecticut: |

How to use a Graphing Calculator to generate random numbers

|Step 1: Go to MATH → PRB |Step 2: Enter the smallest value needed, a comma, then the |When you need multiple values… |

|Choose #5 randInt( |largest value. Hit ENTER to generate a random integer. |Enter the smallest value needed, a comma, the |

| |Note: If you need more than one value, continue hitting |largest value, another comma, and the number |

| |ENTER. Also, Random values may repeat. |of values you want to appear on the screen at |

| | |one time. Then hit ENTER. |

|Step 1: Go to MATH → PRB |[pic] |

|Choose #5 randInt( |Step 2: Enter the smallest value needed, a comma, the largest value, a comma, the number of terms needed,|

| |and ). Then hit STO L1. |

| |(This example stores 100 random integers from 0 to 1 in L1 to |

| |simulate the toss of a coin.) |

PRACTICE: We want to flip a coin to figure out the probability of getting H vs. T.

Before we start, what is the theoretical probability of these two events? P(H) = ½ P(T) = ½

To do this ourselves, we would have to actually flip the coin. Flip a coin 10 times and record your results. What did we get as our experimental probability P(H)? P(H) =

Since we know that the more trials we have, the closer our experimental value will be to the theoretical value, we know that we will need to complete more trials. English statistician Karl Pearson tossed a coin 24,000 times to get the results 12,012 H and 11,988 T. Even this only gives us a P(H) = .5005. We aren’t going to do this many trials, but it is still useful to have another method to help us with problems like these.

With a Number Table: We are going to use the table in our textbook to the right to find the experimental probability that the outcome of a coin toss is H.

1. Which numbers will represent which outcomes? Explain.

2. Simulate 25 trails and record your results. Number of H =

Use your results to calculate P(H) =

3. Simulate another 25 trails and record your results. Number of H =

Use your results to calculate P(H) =

With a graphing calculator: We are going to use the graphing calculator to find the experimental probability that the outcome of a coin toss is H.

1. Which numbers will represent which outcomes? Explain.

2. Simulate 25 trails and record your results. Number of H =

Use your results to calculate P(H) =

3. Simulate another 25 trails and record your results. Number of H =

Use your results to calculate P(H) =

Which method do you prefer? Why?

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