No, p=0.22 or greater occurred in 8% of samples, greater than 5%, so no significant evidence against the 10% claim.
The null hypothesis here would be that the true proportion of purple marbles is 10%, and the alternative hypothesis would be that it's greater than 10%.
Based on the given information:
If the simulated proportion of 0.22 or greater (which represents the proportion of purple marbles) occurred in 8% of samples, it suggests that in 8% of cases, the observed proportion was 0.22 or higher.
If this proportion occurred in 1% of samples, it implies that only 1% of the time did the observed proportion reach 0.22 or more.
In hypothesis testing, a significance level (often denoted as alpha) of 0.05 (or 5%) is commonly used. This signifies the threshold for considering evidence strong enough to reject the null hypothesis.
Considering the options:
The first option suggests that 0.22 or greater occurred in 8% of samples, which is higher than 5%, so it concludes that there's no significant evidence against the null hypothesis.
The second option implies that 0.22 or greater occurred in only 1% of samples, which is lower than 5%, suggesting no significant evidence against the null hypothesis.
The third option aligns with the second option, stating that the occurrence of 0.22 or greater is less than 5%, implying no significant evidence against the null hypothesis.
The fourth option implies that 0.22 or greater occurred in 8% of samples, but the conclusion is that it's less than 5%, suggesting significant evidence against the null hypothesis.
So, based on the principles of hypothesis testing and the significance level commonly used (0.05), the correct answer would align with the third option: "No, p = 0.22 or greater only occurred in 1% of samples in the simulation. Because this is not greater than 5%, they do not have statistically significant evidence that the true proportion of purple marbles in the jar is greater than 10%."