Q-24.
Barron’s reported that the average number of weeks an individual is unemployed is
17.5 weeks. Assume that for the population of all unemployed individuals the population
mean length of unemployment is 17.5 weeks and that the population standard deviation
is 4 weeks. Suppose you would like to select a sample of 50 -unemployed individuals for
a follow-up study.
a. Show the sampling distribution of x, the sample mean average for a sample of
50 unemployed individuals.
b. What is the probability that a simple random sample of 50 unemployed individuals
will provide a sample mean within 1 week of the population mean?
c. What is the probability that a simple random sample of 50 unemployed individuals
will provide a sample mean within 1/2 week of the population mean?
Soln:
sampling distribution of the sample mean average for a sample of 50 unemployed individuals is
approximately normal as sample size is greater then 30
also mean =17.5
and std error of the mean =std deviation/(n)1/2 =4/(50)1/2 =0.5657
probability that a simple random sample of 50 unemployed individuals will provide a sample mean
within 1 week of the population mean =P(17.5-1<X<17.5+1)=P(-1/0.5667<Z<1/0.5667)=P(-
1.7678<Z<1.7678)=0.9615-0.0385
=0.923
Otherway