According to a recent survey, the population distribution of number of years of

Question

According to a recent survey, the population distribution of number of years of education for self-employed individuals in a certain region has a mean of 15.1 and a standard deviation of 2.7. a. Identify the random variable X whose distribution is described here b. Find the mean and the standard deviation of the sampling distribution of x for theta random sample of size 81 interpret them. c. Repeat (b) for n = 324. Describe the effect of increasing n A. The minimum mean for all samples of size 81 ?B. The maximum mean for all samples of size 81 C. The mean of all samples of size 81 D. The expected value for the mean of a sample of size 81 The standard deviation is. (Type an integer or a decimal.) Choose the correct description of the standard deviation. ? A. The maximum deviation of the mean for a sample of size exist1 B. The standard deviation of all samples of size 81 C. The minimum deviation of the mean for a sample of size 81 D. The variability of the mean for samples of size 81 c. The mean of the sampling distribution of size 324 is. (Type an integer or 8 decimal.) The standard deviation is. (Type an integer or 8 decimals.) The mean of the sampling distribution stays the same as n increases. The standard deviation of the sampling distribution decreases as n

Explanation / Answer

Solution:

a) The number of years of education of self-employed individuals in the U.S. has a population mean of 15.1 years and a population standard deviation of 2.7 years.

b) Xbar~N(15.1, 2.7/81) = N(15.1, 0.3) because of the central limit theorem. The average sample
mean of years of education from a sample of 81 self-employed individuals in the US is 15.1
(the same as the population mean of education years) and it this sample of years varies on
average 0.3 years away from this value.

D. The expected value for the mean of a sample size 81

The standard deviation is = 2.7
D. The variability of the mean of sample of size 81

c) Repeat (b) for n = 324. Describe the effect of oincreasing n.
Xbar~N(15.1, 2.7/324) = N(15.1, 0.15) By averaging your sample mean over a larger sample you would reduce your standard deviation by one half. Therefore, we see that quadrupling your
sample size will half your standard deviation of your sample mean.

The mean of the sampling distribution of size 324 is 15.1
The stndard deviation is 2.7
The mean of the sample distribution stays the same as n increases.
The standard deviation of the sampling distribution decreases as n increases.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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