A simple random sample of 60 items resulted in a sample mean of 60, The populati

Question

A simple random sample of 60 items resulted in a sample mean of 60, The population standard deviation is = 10 a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place. b. Assume that the same sample mean was obtained from a sample of 130 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-Select your answermargin of error larger smaller

Explanation / Answer

Solution:

From the given information
Sample mean x = 60
Standard deviation = 10
Sample size n = 60

a) The 95% confidence interval for the population mean
CI = x ± 1.960 (/n)
= 60 ± 1.960 (10/60)
= 60 ± 2.5303
= (57.4697, 62.5303)

b) Assume that the sample sample mean was from a sample of 130 items
The 95% confidence interval for the population mean
CI = x ± 1.960 (/n)
= 60 ± 1.960 (10/130)
= 60 ± 1.7190
= (58.2810, 61.7190)

c) Larger sample provides a smaller margin of error.

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