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.
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)
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