A game is played by rolling balls up a ramp into holes of various point values. A player believes that her mean score at a local arcade is greater than her mean score at an amusement park. She plays 15 games at the arcade and 10 games at the amusement park. Assume those games are a random sample of her true score at both places. Her scores are:

Arcade: 240, 270, 310, 450, 280, 360, 280, 340, 410, 380, 320, 300, 280, 250, 420

Amusement park: 150, 200, 250, 180, 220, 250, 180, 220, 300, 260

Check the conditions for this two-sample test:
1. Games are independent random samples of her true score at the arcade and amusement park.
2. Data are from two groups in a randomized experiment.
3. 15 < 10% of all games she could play at the arcade, and 10 < 10% of all games she could play at the amusement park.
4. The distribution of scores at the arcade has no outliers and no strong skewness.
5. The distribution of scores at the amusement park has no outliers and no strong skewness.
6. The normal/large sample condition is not met.

The conditions for this two-sample game are independent random samples of her true score at the arcade and amusement park. The 10% condition is met for both groups. The distribution of scores at the arcade and amusement park has no outliers and no strong skewness. However, the normal/large sample condition is not met.

To perform a two-sample comparison, certain conditions need to be met. Let's analyze each condition based on the given information:

Independent Random Samples: The games played at the arcade and amusement park are described as random samples. This means that the scores obtained in each location are independent of each other.

10% Condition: The number of games played at the arcade (15) is less than 10% of all the games she could play at the arcade, and the number of games played at the amusement park (10) is less than 10% of all the games she could play there. Thus, the 10% condition is satisfied for both groups.

Distribution of Scores: There is no mention of outliers or a strong skewness in the distribution of scores at either the arcade or the amusement park. Therefore, we can assume that there are no outliers and no strong skewness in the data for both groups.

Normal/Large Sample Condition: The normal/large sample condition is not explicitly mentioned in the given information. Without additional details, we cannot determine whether this condition is met or not.

Based on the given information, the conditions for independent random samples and the 10% condition are met for both groups. However, we do not have enough information to determine whether the normal/large sample condition is met.

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