A simple random sample of 10 items resulted in a sample mean of 30. The populati

Question

A simple random sample of 10 items resulted in a sample mean of 30. The population standard deviation is sigma = 10. 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

Solution:

a) = 0.05, |Z(0.025)|=1.96 (check standard normal table)
So 95% CI is
xbar ± Z*s/n

--> 30 ± 1.96*10/sqrt(10)

--> ( 23.8019358, 36.1980642)

b) So 95% CI is
xbar ± Z*s/n

--> 30 ± 1.96*15/sqrt(100)

--> (27.06, 32.94)

c) As the sample size increases, the confidence interval narrows down.

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