If the random error in the arithmetic mean of 50 observations is \( \alpha \), then the random e...

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If the random error in the arithmetic mean of 50 observations is \( \alpha \), then the random error in the arithmetic mean of 150 observations would be
(a) \( \alpha \)
(b) \( 3 \alpha \)
(c) \( \frac{\alpha}{3} \)
(d) \( 2 \alpha \)
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