Chapter PV, Problem 7RE

(a)

To determine

To explain what the margin of error means in this context.

Explanation of Solution

It is given in the question that using a computer to play many simulated games of scrabble researcher Charles found that the letter “A” occurred in $54\%$ of the hands. This study had a margin of error of $\pm 10\%$ . Thus, we can say that in this context the margin of error is the amount by which the statistics varies assuming a normal sampling distribution which ranges by $54\%\pm 10\%$ .

(b)

To determine

To explain why might the margin of error be so large.

Explanation of Solution

It is given in the question that using a computer to play many simulated games of scrabble researcher Charles found that the letter “A” occurred in $54\%$ of the hands. This study had a margin of error of $\pm 10\%$ . Thus, the margin of error might be so large because the inherent assumption about the model that the success or failure condition is met may not be true or since margin of error is high and it follows that the standard error SE must be large and $SE\propto \frac{1}{\sqrt{n}}$ then n may be too low.

(c)

To determine

To explain does this make you concerned that the simulation might be faulty.

Answer to Problem 7RE

No, it does not make.

Explanation of Solution

It is given in the question that using a computer to play many simulated games of scrabble researcher Charles found that the letter “A” occurred in $54\%$ of the hands. This study had a margin of error of $\pm 10\%$ . Thus, no, this does not make us concerned that the simulation might be faulty because the observation is within the reported interval of $\pm 10\%$ and is not remarkable.