What is the probability the sample mean will be within $1,000 of the population mean

During the first quarter of 2003, the price / earnings ratio for stocks listed on the new york stock exchange generally ranged from 5 to 60. assume that we want to estimate the population mean price/earnings ratio for all stocks listed on the exchange. how many stocks should be included in the sample if we want a margin of error of 3? use 95% confidence.

An online survey by sharebuilder, a retirement plan provider, and harris interactive reported that 60% of female business owners are not confident they are saving enough for retirement. suppose we would like to do a folow-up study to determine how much female business owners are saving each year toward retirement and want to use $100 as a desired margin of error for an interval estimate of the population mean. Use $1100 as a planning value for the standard deviation and recommend a sample size for each of the following situations.
a) a 90% confidence interval is desired for the mean amount saved.
b) a 95% confidence interval is desired for the mean amount saved.
c) a 99% confidence interval is desired for the mean amount saved.
d) when the desired margin of error is set, what happens to the sample size as the confidence level is increased? would you recommend using a 99% confidence interval in this case?

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. what is the planning value for the population standard deviation? how large a sample shold be taken if the desired margin of error is
a) $500?
b) $200?
c) $100?
d) would you recommend trying to obtain the $100 margin of error?

Bbusinessweek surveyed MBA alumni 10 years after graduation. one finding was that alumni spend an average of $115.50 per week eating out socially. you have been asked to conduct a follow-up study by taking a sample of 40 of these MBA alumni. Assume the population standard deviation id $35.
a) show the sampling distribution of the mean, the sample mean weekly expenditure for the 40 MBA alumni.
b) what is the probability the sample mean will be within $10 of the population mean?
c) suppose you find a sample mean of $100. what is the probability of finding a sample mean of $100 or less? would you consider this sample to be an unusually low spending group of alumni? why or why not?

The average annual salary for federal government employees in Indiana is $41,979. use this figure as the population mean and assume the population standard deviation is $5,000. suppose that a random sample of 50 federal government employees will be selected from the population.
a) what is the value of the standard error of the mean?
b) what is the probability tha the sample mean will be more than $41,979?
c) what is the probability the sample mean will be within $1,000 of the population mean?
d) how would the probability in part (c) change if the sample size were to increased to 100?

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