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. What is the error bound of 95% confidence interval for the population mean length of engineering conferences? Construct a 95% confidence interval for the population mean length of engineering conferences. What is the lower bound? Construct a 95% confidence interval for the population mean length of engineering conferences. What is the upper bound?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 3.94

sample standard deviation = s = 1.28

sample size = n = 84

Degrees of freedom = df = n - 1 = 83

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,83 = 1.989

Margin of error = E = t_/2,df * (s /n)

= 1.989 * (1.28 / 84)

= 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

The lower bound is 3.66

The upper bound is 4.22