A simple random sample of 50 items resulted in a sample mean of 20. The populati

Question

A simple random sample of 50 items resulted in a sample mean of 20. The population standard deviation is = 15. a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place. Enter your answer using parentheses and a comma, in the form (n1,n2). Do not use commas in your numerical answer (i.e. use 1200 instead of 1,200, etc.) b. Assume that the same sample mean was obtained from a sample of 100 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places. c. What is the effect of a larger sample size on the interval estimate? Larger sample provides a margin of error.

Explanation / Answer

a) here std error of mean =std deviation/(n)1/2 =15/(50)1/2 =2.1213

for 95% CI ; z=1.96

margin of error =z*std error =4.1577

therefore 95% confidence interval for the population mean =sample mean -/+ margin of error =15.8423 to 24.1577

b)

std error of mean =std deviation/(n)1/2 =15/(100)1/2 =1.5

for 95% CI ; z=1.96

margin of error =z*std error =2.9399

therefore 95% confidence interval for the population mean =sample mean -/+ margin of error =17.0601 to 22.9399

c) Larger sample provides a smaller margin of error

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