Chapter 11.2, Problem 26E

(a)

To determine

To find: The simulation.

Answer to Problem 26E

The maker’s claim is most likely false.

Explanation of Solution

Given:

Simulation involving trials of rolling the actual die and getting a four.

Calculation:

The maker’s claim, or hypothesis, is “the die does not favor any number.” This is the same as saying that the proportion of getting four rolled, in the long run, is $0.16\left(P\left(x=4\right)=\frac{1}{6}\right).$

So, assume the probability of rolling an four is $0.16$ . Simulate the rolling of the die by repeatedly drawing $200$ random samples of size $50$ from a population of $16\%$ ones and $50\%$ zeros. Let the population of ones represent the event of rolling the number four and make a histogram of the distribution of the sample proportions.

  

If on rolling the actual coin $50$ times, $20$ times four is obtained.

Getting $20$ fours in $50$ times rolling a die corresponds to a proportion $\frac{20}{50}=0.40$ . In the simulation, the result had no relative frequency. Because getting $20$ fours is highly unlikely, you can conclude that the maker’s claim is most likely false.

Conclusion:

Hence, the maker’s claim is most likely false.

(b)

To determine

To find: The conclusion when we roll the actual die $50$ times and get $20$ fours.

Answer to Problem 26E

The maker’s claim is most likely true.

Explanation of Solution

Given:

Simulation involving trials of rolling the actual die and getting a four.

Calculation:

If on rolling the actual coin $50$ times, $7$ times four is obtained.

Getting $7$ fours in $50$ times rolling a die corresponds to a proportion $\frac{7}{50}=0.14$ . In the simulation, the result had a relative frequency o $0.16$ f . Because most of the results are close to $0.40$ , this is very likely. Because getting $7$ fours is highly likely, you can conclude that the maker’s claim is most likely true.

Conclusion:

Hence, the maker’s claim is most likely true.