On-Time Airlines. From the FlightStats On-time Performance Report Summary, we found that, in July 2013, the top five North American airlines in terms of percentage of on-time arrivals were Hawaiian (H), Horizon (Z), Compass (C), Alaska (A), and Jazz (J).

(a) List the 10 possible samples ( without replacement ) of size 3 that can be obtained from the population of five airlines. Use the parenthetical abbreviations in your list.

(b) If a simple random sampling procedure is used to obtain a sample of three of these five airlines, what are the chances that it is the first sample on your list in part (a) ? the second sample? the tenth sample?

(c) Describe three methods for obtaining a simple random sample of three of these five airlines.

(d) Use one of the methods that you described in part (c) to obtain a simple random sample of three of these five airlines.

The given statement is:

In terms of percentage of on-time arrivals, the top five North American airlines were:

Hawaiian (H), Horizon (Z), Compass (C), Alaska (A), and Jazz (J).

The 10 samples are:

(H, Z, C), (H, Z, A), (H, Z, J), (H, C, A), (H, C, J), (H, A, J), (Z, C, A), (Z, C, J), (Z, A, J), (C, A, J)

Total samples are ten.

Every sample has an equal chance to be selected.

Therefore, the probability that the first sample is selected is:

$$\begin{gathered} =\frac{1}{10} \\ =0.1 \end{gathered}$$

Every sample has an equal chance to be selected. Therefore the chance that the second sample is selected is 1.

Similarly, the probability that the second sample is selected is:

$$\begin{gathered} =\frac{1}{10} \\ =0.1 \end{gathered}$$

In the same way, the chance that the tenth sample is selected is 1.

Therefore, the probability that the tenth sample is selected is:

$$\begin{gathered} =\frac{1}{10} \\ =0.1 \end{gathered}$$

Method 1:

Take five slips of paper and fold them in half. Each airline should be written on each slip, and three slips should be chosen at random to make a sample of size three.

Method 2:

Pick three airlines at random using a random number generator.

Method 3:

Take ten slips of paper and fold them in half. Part (a) specifies how to write each airline combination. To make a three-size sample, draw a slip at random.

Using MINITAB, create a three-size random sample from five airlines.

PROCEDURE FOR MINITAB:

Step 1: Select Calc > Random Data > Integer from the menu bar.

Step 2: Twice your selected sample size in the Number of rows of data to create a section, just in case there are repeats. Enter 2 as the sample size.

Step 3: In the Store the column, type Sample in column C1.

Step 4: Enter 1 as the minimum value.

Step 5: Enter 5 as the maximum value.

Step 6: Select OK from the drop-down menu.

MINITAB output:

The resulted Sample is: 4 1 2