Chapter 5.1, Problem 12E

(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 there is a game of scribble in which each player has to select the seven tiles from a bag of tiles. Now, we have $100$ tiles: $\text{42 vowels, 56 consonants and 2 blank tiles}\text{.}$

  $\text{7 of the 100}$ tiles are selected. Thus, we assign a unique number from $\text{00 to 41}$ to each vowel tiles, we assign a unique number from $\text{42 to 97}$ to each consonant tiles and we assign $\text{98 and 99}$ to the two blank tiles.

Now, we choose a row from the random digits table. We then select the corresponding tile. We will repeat until you have selected seven tiles.

(b)

To determine

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

Explanation of Solution

In the question there is a game of scribble in which each player has to select the seven tiles from a bag of tiles. Now, we have $100$ tiles: $\text{42 vowels, 56 consonants and 2 blank tiles}\text{.}$

  $\text{7 of the 100}$ tiles are selected. Thus, we assign a unique number from $\text{00 to 41}$ to each vowel tiles, we assign a unique number from $\text{42 to 97}$ to each consonant tiles and we assign $\text{98 and 99}$ to the two blank tiles.

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

  $00694,05977,19664,65441,20903,62371,22725,53340$

Now we select the first two-digit number. Then select the corresponding tile and repeat until you have selected seven unique tiles. So, we have,

  $\begin{array}{l}00\Rightarrow \text{ Select tile00}\\ 69\Rightarrow \text{ Select tile}69\\ 40\Rightarrow \text{ Select tile}40\\ 59\Rightarrow \text{ Select tile}59\\ 77\Rightarrow \text{ Select tile}77\\ 19\Rightarrow \text{ Select tile}19\\ 66\Rightarrow \text{ Select tile}66\end{array}$

Thus we then note that the sample contains tiles $00,69,40,59,77,19,66$ while only tiles $\text{00,40 and 19}$ are vowel tiles.

(c)

To determine

To explain does thus result gives convincing evidence that the bag of tiles was not well mixed.

Answer to Problem 12E

Yes, there is convincing evidence.

Explanation of Solution

In the question there is a game of scribble in which each player has to select the seven tiles from a bag of tiles. Now, we have $100$ tiles: $\text{42 vowels, 56 consonants and 2 blank tiles}\text{.}$ Given that $\text{2 out of 1000}$ trials of the simulation results in all seven tiles being vowels. Since there are only a very few trials that resulted in all seven tiles being vowels, it is likely to obtain that all seven tiles are vowels and thus there is convincing evidence that the bag was not well mixed.