In: Statistics and Probability
A simple random sample of 60 items resulted in a sample mean of 65. The population standard deviation is 16. a. Compute the 95% confidence interval for the population mean (to 1 decimal). ( , ) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals). ( , ) c. What is the effect of a larger sample size on the margin of error?
3 diff Answers
Solution :
Given that,
Point estimate = sample mean = = 65
Population standard deviation = = 16
Sample size = n = 60
Z/2 = 1.96
Margin of error = E = Z/2* ( /n)
= 1.96 * (16 / 60)
= 4.05
At 95% confidence interval estimate of the population mean is,
- E < < + E
65 - 4.05 < < 65 + 4.05
60.95 < < 69.05
( 60.95 , 69.05)
Sample size = n = 60
Margin of error = E = Z/2* ( /n)
= 1.96 * (16 / 120)
= 2.86
At 95% confidence interval estimate of the population mean is,
- E < < + E
65 - 2.86 < < 65 + 2.86
62.14 < < 67.86
( 62.14 , 67.86)
the effect of a larger sample size on the margin of error will decreases