Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the underlying population is normal.
A. What is the error bound of 95% confidence interval for the population mean length of engineering conferences? (Round to 3 decimal places)
B. Construct a 95% confidence interval for the population mean length of engineering conferences.
What is the lower bound? (Round to 2 decimal places)
(c) Construct a 95% confidence interval for the population mean length of engineering conferences.
What is the upper bound? (Round to 2 decimal places)
Solution :
degrees of freedom = n - 1 = 84 - 1 = 83
t/2,df
= t0.025,83 = 1.989
A) Margin of error = E = t/2,df
* (s /
n)
= 1.989 * (1.28 /
84)
Margin of error = E = 0.28
The 95% confidence interval estimate of the population mean is,
- E <
<
+ E
3.94 - 0.28 < < 3.94 + 0.28
( 3.66 <
< 4.22 )
B) lower limit = 3.66 days
C) upper limit = 4.22 days
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