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Question 2, 7.2.33
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A certain deck of cards has cards that show one of five different shapes with equal representation, so that the probability of selecting any particular shape is 0.20 . A card is selected randomly, and a person is asked to guess which card has been chosen. The attached graphs show a computer simulation of experiments in which a "person" was asked to guess which card had been selected in a large number of trials. Each dot in the dotplots represents the proportion of successes for one person. One dotplot represents an experiment in which each person had 10 trials; another shows 20 trials; and a third shows 40 trials. Explain how you can tell, from the widths of the graphs, which has the largest sample $(n=40)$ and which has the smallest sample $(n=10)$.
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Graph has the largest sample size because it has the of the three graphs. Graph has the smallest sample size because it has the of the three graphs.
Answer
Final Answer: The graph with the largest sample size should have the smallest width, and the graph with the smallest sample size should have the largest width. This is because as the sample size increases, the variability of the sample proportion decreases.
Step 1 ：The question is asking to explain how we can tell from the widths of the graphs which has the largest sample size and which has the smallest sample size.
Step 2 ：In general, as the sample size increases, the variability of the sample proportion decreases. This means that the spread or width of the graph should decrease as the sample size increases.
Step 3 ：Therefore, the graph with the largest sample size should have the smallest width, and the graph with the smallest sample size should have the largest width.
Step 4 ：However, without the actual graphs, it's impossible to definitively answer this question.
Step 5 ：Final Answer: The graph with the largest sample size should have the smallest width, and the graph with the smallest sample size should have the largest width. This is because as the sample size increases, the variability of the sample proportion decreases.
