Question

A scientist measured the speed of light. His values are in​ km/sec and have​ 299,000 subtracted from them. He reported the results of 22 trials with a mean of 756.24 and a standard deviation of 119.66.

​a) Find a 90​% confidence interval for the true speed of light from these statistics.

Answer 1

Solution:

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 756.24

S = 119.66

n = 22

df = n – 1 = 21

Confidence level = 90%

Critical t value = 1.7207

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 756.24 ± 1.7207*119.66/sqrt(22)

Confidence interval = 756.24 ± 43.8989

Lower limit = 756.24 - 43.8989 = 712.34

Upper limit = 756.24 + 43.8989 = 800.14

Confidence interval = (712.34, 800.14)

A 90​% confidence interval for the true speed of light from these statistics is given as below:

Confidence interval = (299000+712.34, 800.14)

Confidence interval = (299712, 800.14)