Charles claims he can act as a random number generator. Samantha has doubts. She tells Charles to write down 50 random digits, suspecting that he won't write down 50 random digits, suspecting that Charles produces fewer zeros than the expected 10%? Samantha simulated 100 trails of choosing 50 random digits, assuming that zero has a 1/10 chance of occurring each time. The dotplot shows the number of zeros in each trial. A) Explain how the graph illustrates chance variation. B) Based on the results of the simulation, is there convincing evidence that Charles doesn't choose zero often enough when he's trying to generate random number? Explain.

Question

Charles claims he can act as a random number generator. Samantha has doubts. She tells Charles to write down 50 random digits, suspecting that he won't write down 50 random digits, suspecting that Charles produces fewer zeros than the expected 10%? Samantha simulated 100 trails of choosing 50 random digits, assuming that zero has a 1/10 chance of occurring each time. The dotplot shows the number of zeros in each trial. A) Explain how the graph illustrates chance variation. B) Based on the results of the simulation, is there convincing evidence that Charles doesn't choose zero often enough when he's trying to generate random number? Explain.

Answer 1

A) The dotplot in this scenario illustrates chance variation by showing the distribution of the number of zeros in each trial. It provides a visual representation of the possible outcomes and the frequency of each outcome. Each dot represents one trial, and its position on the graph represents the number of zeros observed in that trial.

B) To determine if there is convincing evidence that Charles doesn't choose zero often enough when generating random numbers, we need to analyze the results of the simulation.

If Charles is truly generating random numbers, we would expect the number of zeros in each trial to vary around the expected proportion of 10%. In other words, the dotplot would show some randomness and chance variation around the expected value.

If the dotplot displays a distribution where the number of zeros consistently falls below 10% in the majority of trials, it would suggest that Charles is indeed not choosing zero as often as he should if he wants to simulate randomness accurately. On the other hand, if the number of zeros falls within an acceptable range around 10% in most trials, it would support Charles' claim of being a random number generator.

To determine if there is convincing evidence, we can calculate summary statistics such as the mean and standard deviation of the number of zeros in the simulated trials. We can also compare the observed proportion of zeros in each trial to the expected proportion of 10% using statistical methods like hypothesis testing or confidence intervals.

Let's analyze the dotplot and calculate the necessary statistics to draw a conclusion.