Question

1. How do you calculate the mean and standard deviation of the sampling distribution for sample means? [2 sentences]
2. What is the effect of increasing sample size on the sampling distribution and what does this mean in terms of the central limit theorem? [2 sentences]
3. Why is the standard deviation of the sampling distribution smaller than the standard deviation of the population from which it came? [3 sentences]

Answer 1

(a)

The mean of the Sampling Distribution of the sampling means = Population Mean

The Standard Deviaion of the Sampling Distribution of the sampling means = Standard Error =

,

where is the standard deviation of the population and n is the sample size.

(b)

By Central Limit Theorem the Sampling Distribution tends to Normal Distribution by increasing sample size.

(c)

The Standard Deviation of the sampling distribution is smaller than the Standard Deviation of the population because of the following reason:

The variation of the sample means in the sampling distribution is smaller than The variation of the individuals in the population. This is because: in the case of sampling distribution, we are concerned with the variations of the sample means in which each sample mean averages together all the data values in the sample. In the case of variation in the population, we are concerned with the how the individual data value differs from the overall mean. Thus, the variation of the means will be smaller than the variation of individuals. This is the reason why the Standard Deviation of the sampling distribution is smaller than the Standard Deviation of the population