Question

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.

PART A:

Construct a 95% confidence interval for the population mean length of engineering conferences.

What is the lower bound of the confidence interval? (Round to 2 decimal places)

PART B:

Construct a 95% confidence interval for the population mean length of engineering conferences.

What is the upper bound of the confidence interval? (Round to 2 decimal places)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 3.94

Population standard deviation =    = 1.28

Sample size = n = 84

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 1.28 /  84 )

= 0.27

At 95% confidence interval estimate of the population mean is,

  ± E

3.94 ± 0.27

( 3.67, 4.21 )  

A) lower bound = 3.67

B) upper bound = 4.21