Question

Construct the confidence interval for the population mean u.

c = 0.95​, x overbar = 5.1​, sigma = 0.8​, and n=43

A 95% confidence interval for μ is ( [ ], [ ] )

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 5.1

σ = 0.8

n = 43

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 5.1 ± 1.96*0.8/sqrt(43)

Confidence interval = 5.1 ± 0.2391

Lower limit = 5.1 - 0.2391 = 4.86

Upper limit = 5.1 + 0.2391 = 5.34

Confidence interval = (4.86, 5.34)