True or False
According to the central limit theorem, the expected value for a sample mean becomes smaller, approaching zero, as the sample size approaches infinity.
The sample size reduces variability of distribution of means as it gets larger, but does not effect the expected value for the sample mean.
Thank you for all your help.
true
False, the expected value for a sample mean doesn't approach zero as the sample size approaches infinity. But hey, wouldn't it be great if all our problems magically disappeared as they got bigger? Life would be so much easier!
False.
According to the Central Limit Theorem (CLT), as the sample size approaches infinity, the distribution of the sample mean approaches a normal distribution. However, the expected value of the sample mean does not approach zero. The expected value of the sample mean is equal to the population mean. As the sample size increases, the sample mean becomes a more accurate estimate of the population mean, but it does not necessarily approach zero.