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.

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)

Answer 1

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