Be specific with your answers i.e. if we give you numbers, use those numbers. If

Question

Be specific with your answers i.e. if we give you numbers, use those numbers. If the distribution of a variable is normal in the population (~N (mu, sigma)), then what shape, mean, and standard deviation does the sampling distribution of the mean have? How does the sample size (n) that we draw from the population affect the shape, center, and spread of the sampling distribution? If the distribution of a variable is very skewed in the population, then what shape, mean, and standard deviation does the sampling distribution of the mean have if samples of size 3 are taken from the population? What are the shape, mean, and standard deviation of the sampling distribution if samples of size 40 are taken?

Explanation / Answer

1. The shape of sampling distribution will be bell shape, mean will be mu and standard deviation, sigma. Mathematiccaly expressed as N(0,1).

2. If repeated random samples of size N are drawn from a normal population with mean mu and standard deviation sigma, then the sampling distribution of sample means will be normal with mean mu and standard deviation sigma/sqrt N.

3. The sampling distribution will have skewed distribution (corresponding to the population), mean will be different from the population mean nad standard deviation will be sigma/sqrt 3.

4. With N=40, mean of the sampling distribution will be closer to population mean, the shape will be roughly normal and standard deviation will be sigma/sqrt 40.

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---

---

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