Financial analyst Larry Potts needs a sample of 100 securities listed on either the New York Stock Exchange (NYSE) or the American Stock Exchange (AMEX). According to the Wall Street Journal's "Stock Market Data Bank," 2,531 NYSE securities and 746 AMEX securities were traded on the previous business day. Larry directs his staff to randomly select 77 NYSE and 23 AMEX securities. His sample is a:

Sampling: Sampling is the method used for population estimates. A sample from the population is chosen, and this forms the population representative. There are various types of sampling used to draw the samples.

Stratified sampling: This is called stratified sampling when the units in the population are divided into subgroups and the sample is then taken from each group. These subgroups are called strata.

The percentages of the sample are equal between each stratum, which is called proportionate stratified sampling. Otherwise, Stratified Sampling is insufficient.

Fundamentals

Procedure for stratified sampling:

1.Select the population from which the sample has to be drawn.

2.Divide the population into homogeneous subgroups based on characteristics of the groups. These subgroups are called as strata.

3.Each unit of the population must be assigned to only one stratum (Subgroup).

4.Now within each stratum select the units using the procedure of the simple random sampling.

5.Combine all the sampled units of the different strata to form the stratified sample.

Step-by-step explanation:

Step 1

The sampling method used is determined below:

From the information, the total number of securities in the New York Stock Exchange (NYSE) is 2,531. The total number of securities in the American Stock Exchange (AMEX) is 746.

Financial analyst selected 100 securities from both NYSE and AMEX called strata. A sample has to be selected from these two strata. The samples selected from the two strata are 77 from NYSE and 23 from AMEX.

There are two different groups, from the each group the sample are selected randomly. This indicates that, stratified random sampling method is used.

Explanation

The type of sampling techniques used in determined using the concept of stratified sampling. The sample is drawn by first dividing the population into groups based on characteristics and then the samples are taken from the two strata NYSE and AMEX.

Step 2

The type of sampling method is obtained as follows:

There are two strata called NYSE and AMEX. The number of securities selected from the NYSE is 77 out of 2,531 and from AMEX is 23 out of 746.

Consider the proportion of sample from each stratum,

\begin{array}{c}\\NYSE = \frac{{77}}{{2531}} = 0.030\\\end{array}  

NYSE=  77 /2531

       =0.030

AMEX=  23/746

            =0.030

The number of samples from each stratum has a same fraction. This indicates that, it is proportionate stratified sampling.

Thus, financial analyst used the proportionate stratified sampling method to collect the sample.

Explanation

The correct sampling method is proportionate or disproportionate is identified by observing the fraction of samples from the two strata is same or not.

Answer

Thus, financial analyst used the proportionate stratified sampling method to collect the sample.

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step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.