A simple random sample of 30 items resulted in a sample mean of 20. The populati

Question

A simple random sample of 30 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 numeical 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 l -Select your answer-margin of error.

Explanation / Answer

The statistical software output for this problem is:

One sample Z summary confidence interval:
: Mean of population
Standard deviation = 15

95% confidence interval results:

95% confidence interval results:

Hence,

a) 95% confidence interval: (14.6, 25.4)

b) 95% confidence interval: (17.1, 22.9)

c) Smaller

Mean n Sample Mean Std. Err. L. Limit U. Limit 30 20 2.7386128 14.632418 25.367582

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