Final answer:
To determine if there is a significant difference between the expected 50 drops and the actual 40 drops from a claimed 5% drop rate, we must calculate the p-value through a statistical hypothesis test. Without performing the specific calculations, we cannot select the correct p-value from the provided choices.
Step-by-step explanation:
A video game claims a 5% drop rate for a certain item. With 100 players attempting to get the drop 10 times each, this results in a total of 1000 attempts. The expected number of drops is 5% of 1000, which is 50 drops. However, the actual result was 40 successful drops. To analyze whether this discrepancy is statistically significant, we use a statistical test to find the p-value that corresponds to the observed results under the assumption that the true drop rate is as claimed.
Comparing alpha (α) and the p-value to make a decision:
- If α is 0.01 (1%) and the p-value is extremely small (much lower than 0.01), like 0.000006, we have strong evidence against the null hypothesis, suggesting it should be rejected.
- If α is 0.05 (5%) and our p-value, for instance, is 0.3430, which is much higher than 0.05, we cannot reject the null hypothesis as we do not have strong evidence against it.
- Generally, if the p-value is lower than α, we reject the null hypothesis. Conversely, if the p-value is higher, we fail to reject the null hypothesis.
In this case, with 40 successful drops instead of the expected 50, we would conduct a hypothesis test (such as a chi-square goodness-of-fit test or a binomial test) to calculate the specific p-value. However, since the provided information and choices do not match our situation precisely, it is not possible to select the correct p-value without performing the specific statistical calculations based on the given results.