Question

The sampling distribution of X   must be a normal distribution The sampling distribution of X   must be a normal distribution. T /F

The standard deviation of the sampling distribution of the sample mean increases as the sample size increases. T/F

Answer 1

False. The sampling distribution of X might not be a normal distribution if the sample size is small. According to Central Limit Theorem, the sampling distribution of the mean of any random variable which is independent will be a normal distribution in case the size of the sample is large.

False. For larger samples, the spread is small. The standard deviation of the sampling distribution of the sample mean decreases as the sample size increases. The standard deviation will increase with a decrease in sample size.