Answer :
A player has played 15 games at a local arcade and 10 games at an amusement park, with the belief that her mean score at the arcade is greater than her mean score at the amusement park.
To determine whether the player's belief is supported by the data, we need to compare the mean scores at the arcade and the amusement park. Let's assume the scores for the arcade games are: 10, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28. And the scores for the amusement park games are: 8, 9, 10, 12, 14, 15, 16, 18, 19, 20.
To find the mean score for each set of games, we sum up the scores and divide by the number of games. For the arcade games, the sum is 334, and the mean score is 334 / 15 = 22.27. For the amusement park games, the sum is 141, and the mean score is 141 / 10 = 14.1.
Comparing the mean scores, we see that the mean score at the arcade (22.27) is indeed greater than the mean score at the amusement park (14.1). Therefore, the player's belief that her mean score at the arcade is greater than her mean score at the amusement park is supported by the given data.
By calculating the mean scores for the games played at the arcade and the amusement park, we can compare the average performance at each location. The mean score is calculated by summing up the scores and dividing by the number of games played.
In this case, the mean score at the arcade (22.27) is higher than the mean score at the amusement park (14.1), suggesting that the player performs better on average at the arcade. This analysis supports the player's belief that her mean score at the arcade is greater than her mean score at the amusement park.
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