Consider the basic sample only create standardizations

Question

Several questions refer to the Basic Sample: persons whose age is in the 21-27 (inclusive) range, who are working at least 40 hours per.

1. Consider the Basic Sample only. Create standardizations (z-scores) of for the variables: wages, age, education, and hours. Display the resulting histograms and statistics next to the unstandardized versions. Describe the main ways the pairs of graphs are similar, and the main ways they are different.
2. Start with the entire data set and construct the variable "zwages1" by (i) restricting your sample to the Basic Sample, and then (ii) forming the z-scores of the wages. Now start with the entire data set and construct "zwages2" by (i) forming the z-scores of the wages, and then (ii) restricting your sample to the Basic Sample. Compare the resulting histogram and statistics, and compare the first observation in the two cases. Explain the differences.
3. Determine the following proportions of persons in the Basic Sample:
   1. Women;
   2. Persons making over 50k;
   3. Persons who are women making over 50k;
   4. Persons who are women or who make over 50k;
   5. The proportion of women among the persons making over 50k;
   6. The proportion of women who make over 50k;

[Hint: Construct the relevant binary (indicator) variables, and them both, and then use N-way tabulation. Intuitively, you will be calculating Pr[A], Pr[B], Pr[A and B], Pr[A or B], Pr[A|B], and Pr[B|A].]

1. The 2016 federal poverty level for family of size 1 (i.e., just you living alone) is $11,770. For a family of size 2 or 3 it is $15,930 and $20,090 respectively. Construct a graph that displays the breakdown of people's wages (ignoring other possible sources of income) in terms of positive and negative percentages (or proportions) above or below the poverty level for a family of size 1. Assuming that each individual is the sole earner for their family, do the same for families of size 2 and 3 (i.e., assume each individual is the sole earner for a family of the appropriate size). Repeat this, but for the Basic Sample only.
2. Restrict your sample to people working at least 40 hours per week (no other constraints). Construct and compare the "histogram and statistics" of wages of 20-25 year olds, 26-35 year olds, 36-45 year olds, 46 - 55 year olds, 56 - 65 year olds, 66 - 70 year olds, and 71+ year olds. What do you notice about wages? Give a short explanation of what you think accounts for the differences in wages. [Copy and paste your histograms and statistics onto a single sheet of paper.]