A simple random sample of 10 items resulted in a sample mean of 40. The populati

Question

A simple random sample of 10 items resulted in a sample mean of 40. The population standard deviation is 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? Do Larger sample provides a LARGER or SMALLER margin of error?

Explanation / Answer

a.
Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=40
Standard deviation( sd )=10
Sample Size(n)=10
Confidence Interval = [ 40 ± Z a/2 ( 10/ Sqrt ( 10) ) ]
= [ 40 - 1.96 * (3.162) , 40 + 1.96 * (3.162) ]
= [ 33.802,46.198 ]

b.
Sample Size(n)=100
Confidence Interval = [ 40 ± Z a/2 ( 10/ Sqrt ( 100) ) ]
= [ 40 - 1.96 * (1) , 40 + 1.96 * (1) ]
= [ 38.04,41.96 ]

c.
Larger provides smaller margin of error

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