To analyze the simulation results and determine whether Marcus can reject the null hypothesis that he will score no more than 6 goals out of 10 attempts, we should first summarize the information provided in the frequency distribution of successful goals scored:
- Total simulations = 100
- Goals scored (successful attempts) ranging from 0 to 10, with the corresponding frequencies as follows:
- 0 goals: 0 times
- 1 goal: 1 time
- 2 goals: 2 times
- 3 goals: 2 times
- 4 goals: 1 time
- 5 goals: 0 times
- 6 goals: 1 time
- 7 goals: 18 times
- 8 goals: 40 times
- 9 goals: 30 times
- 10 goals: 5 times
Now, we need to calculate how many times Marcus scored more than 6 goals. Those frequencies are:
- 7 goals: 18 times
- 8 goals: 40 times
- 9 goals: 30 times
- 10 goals: 5 times
Adding those:
- Total number of times scored more than 6 goals = 18 + 40 + 30 + 5 = 93.
To calculate the p-value, we first determine the proportion of times he scored more than 6 goals:
\[ \text{Proportion} = \frac{93}{100} = 0.93. \]
Since the null hypothesis posited that he scores no more than 6 goals, we need to find the probability (p-value) of scoring more than 6 goals. The obtained proportion of 0.93 indicates that there is a very high likelihood (93%) of scoring more than 6 goals.
Next, we compare this to the significance level of 0.05:
- If the p-value is close to 0, we would reject the null hypothesis.
- If the p-value is close to 1, we would fail to reject the null hypothesis.
Since we found a high proportion (0.93), it suggests that the p-value is indeed close to 0 (very strong evidence against the null hypothesis of scoring no more than 6 goals).
Thus, Marcus can conclude that he has sufficient evidence to reject the null hypothesis.
The correct answer is: C) The p-value is close to 0. Reject the null hypothesis.