Problem 25E
Ages of selfemployed immigrants. Is selfemployment for immigrant workers a faster route to economic advancement in the country? This was one of the questions studied in research published in the International Journal of Manpower (Vol. 32, 2011). One aspect of the study involved comparing the ages of selfemployed and wageearning immigrants. The researcher found that in Sweden, native wage earners tend to be younger than selfemployed natives. However, immigrant wage earners tend to be older than selfemployed immigrants. This inference was based on summary statistics for male Swedish immigrants shown in the table.
a. Based on the information given, why is it impossible to provide a measure of reliability for the inference “Selfemployed immigrants are younger, on average, than wageearning immigrants in Sweden”?
b. What information do you need to obtain a measure of reliability for the inference, part a?
c. Give a value of the test statistic that would lead you to conclude that the true mean age of selfemployed immigrants is less than the true mean age of wageearning immigrants if you are willing to risk a Type I error rate of .01.
d. Assume that s, the standard deviation of the ages, is the same for both selfemployed and wageearning immigrants. Give an estimate of s that would lead you to conclude that the true mean age of selfemployed immigrants is less than the true mean age of wageearning immigrants using α = .01.
e. Is the true value of s likely to be larger or smaller than the one you calculated in part d?
Solution :
Step 1 of 5:
The given problem explain about ages of selfemployed immigrants.
Given this inference was based on summary statistics for male Swedish immigrants the table is given below.
SelfEmployed Immigrants 
WageEarning Immigrants 

Sample Size 
870 
84875 
Mean Age (years) 
44.88 
46.79 
a). Now we have to find why is it impossible to provide a measure of reliability for the inference “Self Employed immigrants are younger, on average, than Wageearning immigrants in Sweden”.
From the given information no measure of the variability or variance of the data.
Hence we cannot provide a measure of reliability.