Problems not in book: Marital status and job level. We sometimes hear that getti
ID: 3225437 • Letter: P
Question
Problems not in book: Marital status and job level. We sometimes hear that getting married is good for your career. The Table below presents data from one of the studies behind this generalization. To avoid gender effects, the investigators looked only at men. The data describe the marital status and the job level of all 8235 male managers and professionals employed by a large manufacturing firm.1 The firm assigns each position a grade that reflects the value of that particular job to the company. The authors of the study grouped the many job grades into quarters. Grade 1 contains jobs in the lowest quarter of the job grades, and Grade 4 contains those in the highest quarter. Exercises 1 – 8 are based on these data.
1. Marginal distributions. Give (in percents) the two marginal distributions, for marital status and for job grade. Do each of your two sets of percents add to exactly 100%? If not, why not?
2. Percents. What percent of single men hold Grade 1 jobs? What percent of Grade 1 jobs are held by single men?
3. Conditional distribution. Give (in percents) the conditional distribution of job grade among single men. Should your percents add to 100% (up to roundoff error)?
4. Marital status and job grade. One way to see the relationship is to look at who holds Grade 1 jobs. a. There are 874 married men with Grade 1 jobs, and only 58 single men with such jobs. Explain why these counts by themselves don’t describe the relationship between marital status and job grade. b. Find the percent of men in each marital status group who have Grade 1 jobs. Then find the percent in each marital group who have Grade 4 jobs. What do these percents say about the relationship?
5. Give a 99% confidence interval for the proportion of men who hold grade 3 jobs. 1 Sanders Korenman and David Neumark, “Does marriage really make men more productive?” Journal of Human Resources, 26 (1991), pp. 282–307. Homework #10 Business Statistics with Computer Applications II
6. Carry out the chi–square test for the hypothesis of no difference between job grade and marital status. What would be the mean of the test statistic if the null hypothesis were true? The value of the statistic is so far above this mean that you can see at once that it must be highly significant. What is the approximate P–value?
7. Look at the terms of the chi–square statistic and compare observed and expected counts in the cells that contribute the most to chi–square. Based on this and your findings in part 4(b), write a short comparison of the differences in job grade and marital status.
8. Association is not causation. The data show that single men are more likely to hold lower-grade jobs than are married men. We should not conclude that single men can help their career by getting married. What lurking variables might help explain the association between marital status and job grade?
Marital Status Single Married Divorced Widowed Totals Job 1 58 874 955 15 70 20 4,239 Grade 2 222 3,927 34 2,490 10 50 2,396 533 551 126 42 8,235 Totals 337 7,730Explanation / Answer
1. Marginal distributions. Give (in percents) the two marginal distributions, for marital status and for job grade. Do each of your two sets of percents add to exactly 100%? If not, why not?
ANswer :
(2) What percent of single men hold Grade 1 jobs? Pr( Grade 1 if single ) = 58/337 * 100 = 17.21 %
What percent of Grade 1 jobs are held by single men? Pr ( single if grade 1) = 58/ 955 * 100 = 6.073%
(3) Conditional distribution. Give (in percents) the conditional distribution of job grade among single men. Should your percents add to 100% (up to roundoff error)?
Answer
Q.4
a. There are 874 married men with Grade 1 jobs, and only 58 single men with such jobs.
These are just numbers and here it is not known that from how many people these people have these certain qualification. So, these are just a data without revalance and can't be compared with each other.
b. Find the percent of men in each marital status group who have Grade 1 jobs. Then find the percent in each marital group who have Grade 4 jobs. What do these percents say about the relationship?
% of men who have grade 1 Jobs in each marital status group
The values given are the percentage of men in each marital status group who have grade 1 and grade 4 jobs.
We cannot establish any relationship by looking this percentages beacuse in both cases Widowed have highest percentage but we can say that single man have lowesst percentage in grade 4 job which can be interpreted as their unwillingness to join lower job when they are unmarried to pursue their higher goals.
5. Give a 99% confidence interval for the proportion of men who hold grade 3 jobs
so p = 2490/ 8235 = 0.3024
Z99% = 2.575
so 99% confideence interval = p +- Z99% * sqrt [ p* (1-p)/n)]
99% confideence interval = 0.3024 +- 2.575 * sqrt [ 0.3024 * 0.6976/8235]
= (0.2894, 0.3154)
6. Carry out the chi–square test for the hypothesis of no difference between job grade and marital status. What would be the mean of the test statistic if the null hypothesis were true? The value of the statistic is so far above this mean that you can see at once that it must be highly significant. What is the approximate P–value?
Answer :
Observed Value is given in the question.
I am giving Expected value here
Now the Chi - square table for each value
X2 = sum of all aove given values = 67.397
for dF = 9 => X2Critical =16.919
X2 > X2Critical
P -value = 4.921 * 10-11
So , it is very highly significant that means there is significant difference between jobgrade and marital status.
(7) The values for single Marital Status varied very much in comparison to others. All other persons are married once and had responsibility of their spouses so that prompts them to get settle in any job. But, for single people , their career growth is important. When there are no additional responsibility, they never settle for a lower grade job because their is further career improvement jobs they could try.
(8) Yes, association is not causation. There must be various other variabes like career growth, exposure to various new fields, startups started by youth which deviated from such kind of jobs.
Marital Status single 11.60 married 51.48 Divorced 30.24 Widowed 6.69 Total 100.00 Job Grade 1 4.09 2 93.87 3 1.53 4 0.51 100Related Questions
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