Question

A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 21. 4 pounds and a standard deviation of 4.8pounds.If a sampling distribution is created using samples of the amounts of weight lost by 83 people on this diet what would be the standard deviation of the sample distribution of sample means? Round to 2 decimal places if necessary

Answer 1

the standard deviation of the sampling distribution of means equals the standard deviation of the population divided by the square root of the sample size

as follows

$stdSample=\frac{std}{\sqrt{n}}$

where

std= standar deviation=4.8

n= sample=83

$stdSample=\frac{4.8}{\sqrt{83}}$$stdSample=0.52686$

round 2 decimal places

stdSample= 0.53