Question 1 The Bureau of Meteorology of the Australian Government provided the m

Question

Question 1 The Bureau of Meteorology of the Australian Government provided the mean annual rainfall (in millimeters) in Australia 1983-2002 as follows (http://www.bom.gov.au/ climate/change/rain03.txt) 499.2, 555.2, 398.8, 391.9, 453.4, 459.8, 483.7, 417.6, 469.2, 452.4, 499.3, 340.6, 522.8, 469.9, 527.2, 565.5, 584.1, 727.3, 558.6, 338.6 Construct a 99% two-sided confidence interval for the mean annual rainfall. Assume population is approximately normally distributed Round your answers to 2 decimal places.

Explanation / Answer

(1)

n = 20     

x-bar = 485.755     

s = 90.34     

% = 99     

Standard Error, SE = s/n =    90.34/20 = 20.20063811

Degrees of freedom = n - 1 =   20 -1 = 19   

t- score = 2.860934604     

Width of the confidence interval = t * SE =     2.86093460403877 * 20.2006381087331 = 57.79270459

Lower Limit of the confidence interval = x-bar - width =      485.755 - 57.7927045889388 = 427.9622954

Upper Limit of the confidence interval = x-bar + width =      485.755 + 57.7927045889388 = 543.5477046

The 99% confidence interval is [427.96, 543.55]

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