Question
In: Statistics and Probability
A simple random sample of 60 items resulted in a sample mean of 10. The population...
A simple random sample of 60 items resulted in a sample mean of 10. The population standard deviation is 20.
Compute the 95% confidence interval for the population mean. Round to 1 decimal place.
Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round to 2 decimal places.
What is the effect of a larger sample size on the interval estimate? Larger sample provides a larger or smaller margin of error.
Solutions
Expert Solution
95% confidence interval for 
is
- Z *
/ sqrt(n) <
< + Z *
/ sqrt(n)
10 - 1.96 * 20 / sqrt(60) < < 10 + 1.96 * 20
/ sqrt(60)
4.94 < < 15.06
95% CI is ( 4.9 , 15.1 )
95% confidence interval for is
- Z *
/ sqrt(n) <
< + Z *
/ sqrt(n)
10 - 1.96 * 20 / sqrt(120) < < 10 + 1.96 * 20
/ sqrt(120)
6.4 < < 13.6
95% CI is ( 6.4 , 13.6 )
larger sample size reduces width of confidence interval.
Larger sample size provide smaller margin of error.
orchestra answered 1 year agoRelated Solutions
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