Question

1-Let x be the mean of a sample selected from a population.

a. What is the mean of the sampling distribution of x equal to?

b. What is the standard deviation of the sampling distribution of x equal to? Assume n∕N ≤ .05.

2-How does the value of σx change as the sample size increases? Explain.​

3-According to the 2015 Physician Compensation Report by Medscape (a subsidiary of WebMD), American orthopedists earned an average of $421,000 in 2014. Suppose that the mean and standard deviation of the 2014 earnings of all American orthopedists are $421,000 and $90,000, respectively. Let x be the mean 2014 earnings of a random sample of 200 American orthopedists. Find the mean and standard deviation of the sampling distribution of x. Assume n∕N ≤ .05.

Answer 1

(a)

The mean of the Sampling Distribution of is equal to the Population Mean = .

(b)

The Standard Deviation of the Sampling Distribution of = Standard Error =

,

where is the Sd of Population and n is the Sample Size.

2. As the Sample Size = n increases, value of will decrease. With bigger Sample Sizes the Sample Mean becomes a more accurate estimate of the population mean.

3.

= Population Mean = $421,000

= Population SD = $90,000

n = Sample Siz = 200

(i)

Mean of the sampling distribution of = Population mean = $421,000

Standard Deviation of the sampling distribution of = /

                                                                          = 90,000/ = 6363.98