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A random sample of 49 colleges yielded a mean cost of college education of $30,500 per...

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Statistics

A random sample of 49 colleges yielded a mean cost of collegeeducation of $30,500 per year. Assume that the population standarddeviation is $3000 and college costs are normally distributed.

a.) Calculate the standard error of the mean. Round to thehundredth.

b.) Calculate the lower bound for a 90% confidence interval forthe population mean cost of education. Round to the hundredth.

c.) Calculate the upper bound for a 90% confidence interval forthe population mean cost of education. Round to the hundredth

d.) You just constructed a 90% confidence interval for thepopulation mean cost of education. How will the interval change ifwe increase the confidence to 99%?

e.) How large a sample is needed if we wish to estimate thepopulation mean cost of college education within $200 with 90%confidence? Round answer up to the next whole number.

Answer & Explanation Solved by verified expert
4.3 Ratings (778 Votes)
a standard error 3000sqrt49 42847 b sample mean xbar 30500 sample standard deviation 3000 sample size n 49 Given CI level is 90 hence 1 09 01 2 012 005 Zc Z2 16449 ME zc sqrtn ME 16449 3000sqrt49 ME 70496 CI xbar Zc    See Answer
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