Quantitative

Answers Assignment 1:

1-Use the wage data set and answer the following questions:

1.  Report measures of location (位置测度) and dispersion of variables wage, years of experience and years of education.

Answer: The quickest way is to use excel Formulas.

Go to the tab formula, choose insert function, when the window open choose the category “statistical” then all Functions such as “MODE, MEDIAN, Average and VAR (which is variance) appear. Range and standard deviation are not listed among the formulas. For range, you can first find Max and min (with the help of formulas) and then subtract them.  For standard deviation, you can calculate the square root of variance by function SQRT. Below is the results:

1.    Among measures of location which of them is the most appropriate representative of these 100 employee’s wage in your opinion?

As we see the range and variance of wage is high, so mean is not a good indicator and median gives a better insight. 

1. Draw the histogram, pie chart and cumulative frequency distribution for wage.

The point is that you should first define some classes and show the frequency of numbers in each class.  Number of classes may vary based your purpose, but it is recommended that the number of classes be the smallest number “K”  such that 2K is greater than the number of observations(n). In this example 99 workers were studied so n=99. If we try k= 6 which means we would have 6 classes, then 26= 64 somewhat less than 99. Hence, 6 is not enough classes. If we let k=7, then 27=128 which is greater than 99. So the recommended number of classes is 7. However, as I said this is not a strict rule and you may define classes more or less than this number, but you should justify your choice and be logical.

Then to calculate the class intervals: divide the range by the number of classes.

For this example, I would choose 6 classes like:

0-3, 4-7, 8-11, 12-15, 16-19, 20-23

Then count the number of observations for each class and draw charts and graphs.

Drawing charts and graphs can be done by the help of excel function: insert/  charts.

Based on the above data set, what is the probability of having an hourly wage of higher than 4 $ with 12 years of education?

This is in fact a conditional probability. You want to know the probability of having wage of higher than 4 under the condition that the person has 12 education.

P( having wage higher than 4| have 12 years of  education)=

[pic 1]

1. Suppose that 40% of Master students at GEM are women. You randomly select 5, and record the number of women in the sample.

1.  Define the random variable.

The random variable is the number of women among these 5 students, since it is not a certain event we do not know how many women we will have.

1.  What are possible values of the random variable?

0,1,2,3,4,5

1.  Find out the probability distribution of the random variable.

It means that for all possible values of X calculate P(x). sum of all these values should equal to 1.

P(0)+ P(1)+ P(2) +P(3) +P(4) +P(5)=1

      P(x)= [pic 2]

P(0)== 0,07776[pic 3]

P(1)==0,2592[pic 4]

P(2)==0,3456[pic 5]

P(3)==0,2304[pic 6]

P(4)==0,0768[pic 7]

P(5)==0,01024[pic 8]

• To calculate each line you can use excel function: insert formula, statistical, binomial.

1. A local club plans to invest $10000 to host a baseball game. They expect to sell tickets worth $20000. But if it rains on the day of game, they won't sell any tickets and the club will lose all the money invested. If the weather forecast for the day of game is 30% possibility of rain, is this a good investment?

A good investment is the one that yield some profit, meaning that revenues be higher than costs.