A simple random sample of 40 items resulted in a sample mean of 40. The populati
ID: 3125940 • Letter: A
Question
A simple random sample of 40 items resulted in a sample mean of 40. 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 ____________ for margin of error.
Explanation / Answer
Solution :
a) 95% confidence interval for the population mean :
Standard error of the mean is SE = /n = 20/40 =3.1623
For 95% confidence, the critical Z- score is 1.96
Width of the confidence interval is E = z * SE = 1.96 * 3.1623 = 6.1981
The confidence interval is [x-bar - E, x-bar + E]
= [40 - 6.1981, 40 + 6.1981]
= [33.80, 46.20]
b)
Standard error of the mean is SE = /n = 20/130 =1.7541
For 95% confidence, the critical Z- score is 1.96
Width of the confidence interval is E = z * SE = 1.96 * 1.7541 = 3.4381
The confidence interval is [x-bar - E, x-bar + E]
= [40 - 3.4381, 40 + 3.4381]
= [36.57, 43.44]
c) As the sample size increases, the confidence interval narrows down.
Margin of error decreases for larger Sample.
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