You can use technology to simulate experiments with large numbers of trials.
See solution.
Practice makes perfect
We are told that 60 % of all vacationers enjoy water parks. We want to find how closely can 20 random samples of 100 vacationers estimate this percent. First, let's see that we can use technology to simulate experiments with large numbers of trials. Here are the parameters of our simulation.
We are told that the actual percentage of all vacationers who enjoy water parks is 60 %.
The number of samples is 20.
The sample size, which is the number of vacationers in each sample, is 100.
Now, we can use this information to run our simulation. The result is a graph showing the frequencies of each sample percentage — the percent of positive answers in the sample. The higher the bar, the more frequent the sample percentage.
We see that the sample percentages are clustered around 0.6 = 60 %. Also, the majority of the estimates are between 50 % and 70 %, which means that most of the samples are within 10 % of the actual percentage.
60 % - 10 % &= 50 %
60 % + 10 % &=70 %
Note that this just a sample solution. In general, the results of a simulation are different each time we run it, which is why the estimates may also vary.
