Answer true or false and explain. The probability that the average of 20 values

Question

Answer true or false and explain.
The probability that the average of 20 values will be within 0.4 standard deviations of the population mean is larger than the probability that the average of 40 values will be within 0.4 standard deviations of the population mean. Answer true or false and explain.
The probability that the average of 20 values will be within 0.4 standard deviations of the population mean is larger than the probability that the average of 40 values will be within 0.4 standard deviations of the population mean.
The probability that the average of 20 values will be within 0.4 standard deviations of the population mean is larger than the probability that the average of 40 values will be within 0.4 standard deviations of the population mean.

Explanation / Answer

false: as sample size increases std error reduces due to which variation around mean reduces.

Hence for greater sample size, average value is more inclined to remain closer to mean

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