BusinessWeek conducted a survey among students who finished their studies in the

Question

BusinessWeek conducted a survey among students who finished their

studies in the 30 programs of a master's degree (BusinessWeek, September 22,

2003). According to this survey, the average annual salary of a woman and a

Man 10 years after finishing his studies is $ 117,000 and $ 168,000,

respectively. Consider these amounts as the half populations of

wages of a woman and a man. Assume that the standard deviation

population among women's wages is $ 25,000 and among the salaries of

Men is $ 40,000. With this information:

A.         What is the probability that in a simple random sample of 40 men the sample mean did not differ more than $ 10,000 from the average population of $ 168,000?

B.        What is the probability that in a simple random sample of 40 women, the sample mean should not differ more than $ 10,000 from the average population of $ 117,000?

C.        In which of the two cases a) and b) are more likely to obtain a sample mean that does not differ by more than $ 10,000 from the population mean? Why?

D.        What is the probability that in a simple random sample of 100 men, the sample mean should not differ by more than $ 4,000 from the average population?

Explanation / Answer

a)

  probability that in a simple random sample of 40 men the sample mean did not differ more than $ 10,000 from the average population of $ 168,000

b)

c)

in case B as ; stadnard deviation for women wages is less therefore the deviation from mean should be less in comparison than man wages.

d)

for normal distribution z score =(X-)/ here mean=       = 168000.000 std deviation   == 40000.00 sample size       =n= 40 std error=x=/n= 6324.5553

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