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

Question

A simple random sample of 20 items resulted in a sample mean of 30. The population standard deviation is  = 20.

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 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 a - Select your answer -larger or smaller- Item 3 margin of error.

Explanation / Answer

(a)

n = 20     

x-bar = 30     

s = 20     

% = 95     

Standard Error, SE = /n =    20 /20 = 4.472135955

z- score = 1.959963985     

Width of the confidence interval = z * SE =     1.95996398454005 * 4.47213595499958 = 8.765225406

Lower Limit of the confidence interval = x-bar - width =      30 - 8.76522540576582 = 21.23477459

Upper Limit of the confidence interval = x-bar + width =      30 + 8.76522540576582 = 38.76522541

The 95% confidence interval is [21.23, 38.77]

(b)

n = 130     

x-bar = 30     

s = 20     

% = 95     

Standard Error, SE = /Ön =    20 /130 = 1.754116039

z- score = 1.959963985     

Width of the confidence interval = z * SE =     1.95996398454005 * 1.75411603861406 = 3.43800426

Lower Limit of the confidence interval = x-bar - width =      30 - 3.43800426038763 = 26.56199574

Upper Limit of the confidence interval = x-bar + width =      30 + 3.43800426038763 = 33.43800426

The 95% confidence interval is [26.56, 33.44]

(c) Larger sample provides a smaller margin of error.

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