What type of error might we have made? Explain what the error means in the context of the application.

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BlackTom AI · Accepted Answer

First, consider what the question is asking: identify the type of error and explain its meaning in the study context. 
Option 1: 'Type 2 error; In the context of the study, it means deciding that the data provide convincing evidence of a difference between the average reading and writing scores of students when in reality there is no difference.' This describes a false positive, which is the hallmark of a Type 1 error, not a Type 2 error. So this option is incorrect due to mislabeling the error type and mischaracterizing the conclusion. 
Option 2: 'Type 1 error; In the context of the study, it means deciding that the data do not provide convincing evidence of a difference between the average reading and writing scores of students when in reality there is a difference.' Here, the description flips the direction: a Type 1 error corresponds to concluding there is a difference when there isn’t one, not failing to find a difference. Thus this option is incorrect because of both the error type and the conclusion described. 
Option 3: 'Type 2 error; In the context of the study, it means deciding that the data do not provide convincing evidence of a difference between the average reading and writing scores of students when in reality there is a difference.' This accurately captures the essence of a Type 2 error: failing to detect a real difference (a false negative). However, note the option specifies Type 2 but the wording matches a Type 2 error’s meaning, so this option is plausible as a correct description, though its labeling must align with the established terminology. 
Option 4: 'Type 1 error; In the context of the study, it means deciding that the data provide convincing evidence of a difference between the average reading and writing scores of students when in reality there is no difference.' This is the classic definition of a Type 1 error: a false positive where you conclude a difference exists when it does not. The statement correctly describes both the error type and the mistaken conclusion. 
To distinguish between the options, focus on the core definitions: Type 1 = false positive (conclude a difference exists when it does not); Type 2 = false negative (fail to detect a real difference). Options that mislabel the error type or misstate the direction of the conclusion are incorrect, while the option that correctly matches both the error type and the erroneous conclusion aligns with the standard definitions. 
In summary, the incorrect options misrepresent either the error type or the direction of the conclusion, whereas the option that accurately maps Type 1 to a false positive provides a correct conceptual match to the standard statistical testing framework.

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What type of error might we have made? Explain what the error means in the context of the application.

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