# Fundamentals of Statistics

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## 1.5 Sample Selection Methods

Proper sampling can be done with or without replacement.

#### Sampling With Replacement

CONCEPT A sampling method in which each selected item is returned to the frame from which it was selected so that it has the same probability of being selected again.

EXAMPLE Selecting entries from a fishbowl and returning each entry to the fishbowl after it is drawn.

#### Sampling Without Replacement

CONCEPT A sampling method in which each selected item is not returned to the frame from which it was selected. Using this technique, an item can be selected no more than one time.

EXAMPLES Selecting numbers in state lottery games, selecting cards from a deck of cards during games of chance such as Blackjack.

INTERPRETATION Sampling without replacement means that an item can be selected no more than one time. You should choose sampling without replacement over sampling with replacement, because statisticians generally consider the former to produce more desirable samples.

Other, more complex, sampling methods are also used in survey sampling. In a stratified sample, the items in the frame are first subdivided into separate subpopulations, or strata, and a simple random sample is conducted within each of the strata. In a cluster sample, the items in the frame are divided into several clusters so that each cluster is representative of the entire population. A random sampling of clusters is then taken, and all the items in each selected cluster or a sample from each cluster are then studied.

## CALCULATOR KEYS: Entering Data

You can choose one of two ways to enter data values for a variable.

When entering one short list of values for a single variable:

Press [2nd][(] and enter the values separated by commas. (Press [,] to type a comma.) When you finish entering values, press [2nd][)] and enter the name of the variable in which to store the values. For example, to store values in variable L1, press [2nd][1]. Press [ENTER] to complete the data entry. Your calculator will display the values separated by spaces and your screen will look similar to this:

When entering the values for several variables, or many values for a single variable:

Press [STAT]. Select 1:Edit and press [ENTER]. Use the cursor keys to move the cursor to the column of the variable for which you want to enter data. (If you have just cleared your RAM memory, the cursor will be in the column for variable L1.) Enter the first data value and press [ENTER]. Repeat until all values have been entered. Your screen will look similar to this:

You can enter the data values for a second variable by using the cursor keys to move to the column of another variable. To delete values previously entered into a column, move the cursor to the name of variable and press [CLEAR][ENTER].

When you have finished entering all values, press [2nd][MODE] to quit and return to the main display.

If you have a connection cable and the TI Connect software, you can also enter values for a variable using the TI Data Editor application.

## SPREADSHEET SOLUTION: Entering Data

Select FileNew. Select Blank Workbook from the task pane. (If using an older version of Excel, select the Workbook icon in the New dialog box.) Click cell A1. Enter a name for variable in this cell and press [ENTER]. Type the first data value and press [ENTER]. Repeat until all values have been entered. Notice that every time you press [ENTER] the worksheet entry automatically advances down one row.

When you have finished entering data, select FileSave As, type a filename, and click the Save button to save your data.