Barron’s reported that the average number of weeks an individual is unemployed i

Question

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.

Show the sampling distribution of the sample mean average for a sample of 50 unemployed individuals.

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?

Explanation / Answer

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

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