What are the requirements on sampling and the population so that the distributio

Question

What are the requirements on sampling and the population so that the distribution of sample means is approximately normal? [2 bullets] How do you calculate the mean and standard deviation of the sampling distribution for sample means? [2 sentences] 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] Why is the standard deviation of the sampling distribution smaller than the standard deviation of the population from which it came? [3 sentences]

Explanation / Answer

(a) Requirements ar e

(i) )Sample size must be large enough specially more than 30.

(ii) sampling must be simple random sampling.

(b) Here mean of sampling distribution for sample mean would be the sum divided of all sample means by sample size.

Standard deviation of sample means is standard deviation of population (if not given than sample standard deviation) divided by square root of sample size.

(c) Hre if we increase the sample size than it will reduce the standard deviation of sample means and reduce the margin of error., Here in terms of central limit theorem we can say that the distribution of sample means tend to follow the normal distribution where population mean as the mean of that distribution.

(d) Here the term "divided by square root" reduce the standard deviation of the sample means. In layment terms, the standard deviation of sampling distribution has smaller deviation from mean level as compared to large populations.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.