The Bureau of Meteorology of the Australian Government

Chapter 8, Problem 35E

(choose chapter or problem)

QUESTION:

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

Check the assumption of normality in the population. Construct a 95% confidence interval for the mean annual rainfall.

Questions & Answers

QUESTION:

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

Check the assumption of normality in the population. Construct a 95% confidence interval for the mean annual rainfall.

ANSWER:

Step 1 of 3

Given

The annual rainfall (in millimeters) : 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

Sample size, n = 20.

Confidence Interval = 95%

We know that for and s, the mean and standard deviation of a random sample from a normal distribution with unknown variance , a Confidence Interval on is given by,