You have collected weekly earnings data along with some characteristics from a sample of 1,770 individuals using the Current Population Survey in a given year In US. The table below gives you the basic descriptive statistics for your data set:

a)

What relation a-priori would you expect between earnings and place of residence?  Explain clearly why you would expect this relation and discuss whether you think the data confirms your expectations or not ). If not, can you give possible reasons?

 

(b)

Construct a 95% confidence interval for average earnings for workers with attractive apperance. State the meaning of this interval in words. If you were to construct a 90% confidence interval instead, would it be smaller or larger (no need to construct it though)? What is the intuition?

 

(c)

The ConCass Association believes that there is a no discrimination between Males and Females in terms of their earnings. Is there an evidence in the data that the Association is right? Make a relevant statistical analysis, clearly state the hypotheses that you test, the test statistic and its sampling distribution. Use 5% significance level and provide a clear answer to the question. Compute as well a p-value and use it confirm your findings.

 

(d)

The ConCass Association believes that the sample used for the analysis is not a representative one as the Women are under-represented in the sample. The Association points that according to most of the population studies, females account for around 55% of the population. Does the data support the claim of the Association? Make a relevant statistical analysis, clearly state the hypotheses that you test, the test statistic and its sampling distribution. Use 10% significance level and provide a clear answer to the question.

 

Transcribed Image Text:

Average Earnings Standard Deviation Sy N Full sample: $434 $294 1770 Age category: Old (age ≥45) $488 $328 533 Young (age<45) $412 $276 1237 Gender category: Males $502 $316 822 Females $388 $376 948 Education category: With MS degree $456 $395 455 Without MS degree $427 $373 1315 Residence category: City (300 thous.) $432 $323 1072 Town (<300 thous.) $471 $366 698 Appearance: Attractive appearance $493 $382 856 Less-attractive appearance $414 $336 914 Average Earnings Standard Deviation Sy N Full sample: $434 $294 1770 Age category: Old (age ≥45) $488 $328 533 Young (age<45) $412 $276 1237 Gender category: Males $502 $316 822 Females $388 $376 948 Education category: With MS degree $456 $395 455 Without MS degree $427 $373 1315 Residence category: City (300 thous.) $432 $323 1072 Town (<300 thous.) $471 $366 698 Appearance: Attractive appearance $493 $382 856 Less-attractive appearance $414 $336 914

Answer rating: 100% (QA)

Based on the data in the table we can perform some statistical analysis to answer your questions a Earnings and place of residence We can expect a pos... View the full answer