Chapter 5.1, Problem 11E

(a)

To determine

To describe how you would use a table of random digits to carry out this simulation.

Explanation of Solution

In the question the TSA wants to check the security of the passengers by taking out the random sample. We need to describe how we would use a table of random digits to carry out this simulation. Thus, we have $76$ passengers: $12$ in first class and $64$ in coach class. And $\text{10 of the 76}$ passengers are chosen for screening. Then we assign a unique number from $\text{1 to 12}$ to each passengers in first class and we assign a unique number from $\text{13 to 76}$ to each passengers in the coach class.

Now, we choose a row from the random digits table. Then we select the first two-digit number. If the number is between $\text{01 and 76}$ then select the corresponding passenger, else ignore the number and select the next two-digit number. We will repeat it until you have selected ten unique passengers.

(b)

To determine

To perform one trial of the simulation using the random digits given.

Explanation of Solution

In the question the TSA wants to check the security of the passengers by taking out the random sample. Thus, we have $76$ passengers: $12$ in first class and $64$ in coach class. And $\text{10 of the 76}$ passengers are chosen for screening. Then we assign a unique number from $\text{1 to 12}$ to each passengers in first class and we assign a unique number from $\text{13 to 76}$ to each passengers in the coach class.

Now, we choose a row from the random digits table as:

  $71487,09984,29077,14863,61683,47052,62224,51025$

Then we select the first two-digit number. If the number is between $\text{01 and 76}$ then select the corresponding passenger, else ignore the number and select the next two-digit number. We will repeat it until you have selected ten unique passengers. Such as,

  $\begin{array}{l}71\Rightarrow \text{ Select passenger71}\\ 48\Rightarrow \text{ Select passenger}48\\ 70\Rightarrow \text{ Select passenger}70\\ 99\Rightarrow \text{ Ignore}\\ 84\Rightarrow \text{ Ignore}\\ 29\Rightarrow \text{ Select passenger}29\\ 07\Rightarrow \text{ Select passenger}07\\ 71\Rightarrow \text{ Ignore}\\ 48\Rightarrow \text{ Ignore}\\ 63\Rightarrow \text{ Select passenger63}\\ \text{61}\Rightarrow \text{ Select passenger}61\\ 68\Rightarrow \text{ Select passenger}68\\ 34\Rightarrow \text{ Select passenger}34\\ 70\Rightarrow \text{ Ignore}\\ 52\Rightarrow \text{ Select passenger}52\end{array}$

We then note that the sample contains passengers $71,48,70,29,07,63,61,68,34,52$ while only passenger $07$ is a first class passenger.

(c)

To determine

To explain if in $\text{15 of the 100}$ trials of the simulation, none of the ten passengers chosen was seated in the first class does this result provide convincing evidence that the TSA officers did not carry out a truly random selection.

Answer to Problem 11E

No, there is no convincing evidence.

Explanation of Solution

In the question the TSA wants to check the security of the passengers by taking out the random sample. Now, $\text{15 of the 100}$ trials of the simulation results in none of the ten passenger chosen were seated in first class. Since there are many trials that resulted in no first class passengers, it is likely to obtain that no first class passengers are selected and thus there is no convincing evidence that the TSA officers did not carry out a truly random selection.