Question

using the dotplot, is there evidence that the proportion of times a spun dime lands on heads is greater than 0.5?
yes, a proportion of 0.68 proves that the true proportion of heads is greater than 0.5.
yes, a proportion of 0.68 only occurred once out of 100 simulated proportions; therefore, there is sufficient evidence that the true proportion of heads is greater than 0.5.
no, a proportion of 0.68 is only 0.18 more than 0.5; therefore, there is insufficient evidence that the true proportion of heads is greater than 0.5.

Explanation:

To determine if there's evidence the proportion of heads is > 0.5, we analyze the dotplot and options:

• Option 1: A single proportion (0.68) doesn’t “prove” the true proportion—simulation results show variability, and one value isn’t conclusive.
• Option 2: A rare occurrence (once in 100) of 0.68 doesn’t mean the true proportion is > 0.5. Rare events can happen by chance in simulations, and the dotplot likely has many values around 0.5, so 0.68 being rare doesn’t imply a true shift.
• Option 3: The argument about the difference (0.18) is flawed, but the key is that most simulated proportions cluster around 0.5, and a single value (or small difference) isn’t enough to conclude the true proportion is > 0.5. However, re - evaluating the options, the first two are incorrect because a single proportion or its rarity in simulation doesn’t prove the true proportion. The third option’s reasoning about the difference is not the right way, but among the options, the correct conclusion is that there’s insufficient evidence. Wait, no—actually, the dotplot (with n = 25) shows simulated proportions. If most are around 0.5, and 0.68 is an outlier but not enough to conclude the true proportion is > 0.5. But the options: the first two are wrong (a single proportion or its frequency in simulation doesn’t prove the true proportion), and the third’s reasoning is wrong, but the conclusion “No, ... insufficient evidence” is correct because we can’t conclude the true proportion is > 0.5 from a single value or small difference. Wait, no—let's re - check. The question is about evidence from the dotplot. The dotplot likely has a peak around 0.5, so proportions like 0.68 are possible by chance, and we can’t conclude the true proportion is > 0.5. So the correct option is the third one? Wait, no—the third option’s reasoning is “0.68 is only 0.18 more than 0.5; therefore, insufficient evidence”. The reasoning is incorrect (difference size isn’t the right metric), but the conclusion “insufficient evidence” is correct. The first two options are wrong because a single proportion or its rarity in simulation doesn’t prove the true proportion is > 0.5. So the correct answer is the third option: "No, a proportion of 0.68 is only 0.18 more than 0.5; therefore, there is insufficient evidence that the true proportion of heads is greater than 0.5."

Answer:

No, a proportion of 0.68 is only 0.18 more than 0.5; therefore, there is insufficient evidence that the true proportion of heads is greater than 0.5.