The correlation in between mobile usage and exam score of a person found to be -2.2. What is your inference from the above statement.

Question

BlackTom AI · Accepted Answer

Question restatement: The correlation between mobile usage and exam score is reported as -2.2. What inference can be drawn from this statement?

Option 1: 'Mobile usage is negatively correlated with exam score' This would be true if the correlation coefficient r were a valid value ≤ -0.999... however, the correlation coefficient ranges from -1.0 to +1.0. A value of -2.2 falls outside this theoretical bound, indicating a data or reporting error. Therefore, as a standalone inference about the relationship, this statement relies on an impossible statistic and cannot be trusted as a valid conclusion.

Option 2: 'Mobile usage is positively correlated with exam score' A positive correlation would require r > 0. But the reported value is -2.2, which is not only negative but also outside the permissible range. This makes the claim invalid as a factual inference from correlation analysis. It ignores the fundamental constraint on r and would misrepresent the relationship.

Option 3: 'None of the mentioned' This option can be considered a candidate when the given statistic itself is invalid or unusable for drawing standard inferences. Since both Options 1 and 2 rely on an incorrect (out-of-bounds) correlation value, they do not provide legitimate interpretations of the data. The phrase 'None of the mentioned' acknowledges that the listed inferences are not supported by a valid correlation figure.

Option 4: 'Mobile usage is not related to exam score' This implies no relationship (r approximately 0). While this is a possible conclusion in some datasets, it cannot be derived from a corrupted or invalid correlation value such as -2.2. Inferring no relationship would require a properly bounded and reported statistic close to zero, which is not the case here. The invalid value precludes asserting a non-relationship on its own.

Additional observations: In correlation analysis, the coefficient must lie between -1 and 1 inclusive. Values outside this range typically point to data entry mistakes, calculation errors, or miscommunication of the metric (for example, confusing r with a different statistic). Any inference based on an out-of-bounds value should be treated with caution and typically leads to rechecking the data and the method used to compute the correlation.

Summary thought process: When faced with an impossible statistic like -2.2, the most defensible stance is to flag the statistic as invalid and rely on re-evaluating the data and calculation before drawing concrete inferences. Consequently, the conventional inferences expressed in Options 1 and 2 are not supported by a valid correlation value, and Option 3 is the only choice that acknowledges the inconsistency, while Option 4 cannot be justified from the given statistic alone.

The correlation in between mobile usage and exam score of a person found to be -2.2. What is your inference from the above statement.

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类似问题

Of the following, the correlation coefficient that indicates the weakest relationship between the two variables being measured is ______________.

The correlation between temperature in ◦F and age in weeks was r = −0.70. If we converted the temperature to ◦C and age to months, what would the 29 correlation be?

Their correlation coefficients will be the same, since the correlation coefficient is unitless.

r = −0.85

r = −0.03

r = −0.48

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