aianjie

 

15、The probability that an observation lies within three standard deviations of the mean for any probability distribution is at least:

A) 75%.

B) 54%.

C) 89%.

D) 99%.

aianjie

 

The correct answer is C

One can use Chebyshev's Inequality to calculate this proportion. 1 ? (1/32) = 89%.

aianjie

 

AIM 2: Explain the process of sampling from a normal population, and concepts of random sampling, random variables, independently and identically distributed variables, standard error.

1、An equity analyst needs to select a representative sample of manufacturing stocks. Starting with the population of all publicly traded manufacturing stocks, she classifies each stock into one of the 20 industry groups that form the Index of Industrial Production for the manufacturing industry. She then selects a number of stocks from each industry based on its weight in the index. The sampling method the analyst is using is best characterized as:

A) data mining.

B) nonrandom sampling.

C) simple random sampling.

D) stratified random sampling.

aianjie

 

The correct answer is D

In stratified random sampling, a researcher classifies a population into smaller groups based on one or more characteristics, takes a simple random sample from each subgroup based on the size of the subgroup, and pools the results.

aianjie

 

2、An analyst divides the population of U.S. stocks into 10 equally sized sub-samples based on market value of equity. Then he takes a random sample of 50 from each of the 10 sub-samples and pools the data to create a sample of 500. This is an example of:

A) simple random sampling.

B) complex normal sampling.

C) stratified random sampling.

D) systematic cross-sectional sampling.

aianjie

 

The correct answer is C

In stratified random sampling we first divide the population into subgroups, called strata, based on some classification scheme. Then we randomly select a sample from each stratum and pool the results. The size of the samples from each strata is based on the relative size of the strata relative to the population. Simple random sampling is a method of selecting a sample in such a way that each item or person in the population being studied has the same (non-zero) likelihood of being included in the sample.

aianjie

 

3、Joseph Lu calculated the average return on equity for a sample of 64 companies. The sample average is 0.14 and the sample standard deviation is 0.16. The standard error of the mean is closest to:

A) 0.1600.

B) 0.0025.

C) 0.0200.

D) 0.0500.

aianjie

 

The correct answer is C

The standard error of the mean = σ/√n = 0.16/√64 = 0.02.

aianjie

 

4、From a population of 5,000 observations, a sample of n = 100 is selected. Calculate the standard error of the sample mean if the population standard deviation is 50.

A) 4.48.

B) 5.00.

C) 4.00.

D) 50.00.

aianjie

 

The correct answer is B

The standard error of the sample mean equals the standard deviation of the population divided by the square root of the sample size: 50 / 1001/2 = 5.