Question

Note: Each bound should be rounded to three decimal places.

Q: A random sample of n=100 observations produced a mean of x⎯⎯⎯=35 with a standard deviation of s=5.

(a) Find a 95% confidence interval for μ Lower-bound: Upper-bound:

(b) Find a 90% confidence interval for μ Lower-bound: Upper-bound:

(c) Find a 99% confidence interval for μ Lower-bound: Upper-bound:

Answer 1

Ans ) we have given n=100

sample mean =35 with a standard deviation of s=5.

(a) using excel>addin>phstat>confidence interval we have

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	5
Sample Mean	35
Sample Size	100
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.5
Degrees of Freedom	99
t Value	1.9842
Interval Half Width	0.9921
Confidence Interval
Interval Lower Limit	34.008
Interval Upper Limit	35.992

a 95% confidence interval for μ

Lower-bound:34.008

Upper-bound:35.992

(b)

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	5
Sample Mean	35
Sample Size	100
Confidence Level	90%
Intermediate Calculations
Standard Error of the Mean	0.5
Degrees of Freedom	99
t Value	1.6604
Interval Half Width	0.8302
Confidence Interval
Interval Lower Limit	34.170
Interval Upper Limit	35.830

a 90% confidence interval for μ

Lower-bound:34.170

Upper-bound:35.830

(c)

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	5
Sample Mean	35
Sample Size	100
Confidence Level	99%
Intermediate Calculations
Standard Error of the Mean	0.5
Degrees of Freedom	99
t Value	2.6264
Interval Half Width	1.3132
Confidence Interval
Interval Lower Limit	33.687
Interval Upper Limit	36.313

a 99% confidence interval for μ

Lower-bound:33.687

Upper-bound:36.313