Question

Suppose the Annual rainfall (in inches) in 5 different locations in Hawaii are: 12, 21, 14, 16, 17. A statistician wants to use this data to test the claim that the average rainfall in Hawaii is more than 18 inches. Assume significance level α = 0.05 .   

Calculate the 90% Confidence Interval for the average rainfall in Hawaii, show excel commands and formulas used.

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 = 16

S = 3.391164992

n = 5

df = n – 1 = 4

Confidence level = 90%

Critical t value = 2.1318

[by using excel command =TINV(1 - 0.90,4)]

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

Confidence interval = 16 ± 2.1318*3.391164992/sqrt(5)

Confidence interval = 16 ± 3.2331

Lower limit = 16 - 3.2331 = 12.77

Upper limit = 16 + 3.2331 = 19.23

Confidence interval = (12.77, 19.23)