The Bureau of Meteorology of the Australian Government provided the mean annual
ID: 3023928 • Letter: T
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
Compute a 90% prediction interval on the rainfall for the next year. Compare the length of the prediction interval with the length of the 90% confidence interval on the population mean. Round the answers to 3 decimal places.
Explanation / Answer
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
Compute a 90% prediction interval on the rainfall for the next year. Compare the length of the prediction interval with the length of the 90% confidence interval on the population mean. Round the answers to 3 decimal places.
Regression Analysis
r²
0.098
n
20
r
0.313
k
1
Std. Error
88.142
Dep. Var.
rainfall
ANOVA table
Source
SS
df
MS
F
p-value
Regression
15,219.5306
1
15,219.5306
1.96
.1786
Residual
139,841.0589
18
7,768.9477
Total
155,060.5895
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=18)
p-value
90% lower
90% upper
Intercept
435.5232
40.9446
10.637
3.43E-09
364.5227
506.5236
t
4.7840
3.4180
1.400
.1786
-1.1430
10.7110
Predicted values for: rainfall
90% Confidence Interval
90% Prediction Interval
t
Predicted
lower
upper
lower
upper
Leverage
21
535.987
464.986
606.987
367.458
704.516
0.216
90% prediction interval on the rainfall for the next year =(367.458, 704.516)
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
90.3387
Sample Mean
485.755
Sample Size
20
Confidence Level
90%
Intermediate Calculations
Standard Error of the Mean
20.2004
Degrees of Freedom
19
t Value
1.7291
Interval Half Width
34.9291
Confidence Interval
Interval Lower Limit
450.826
Interval Upper Limit
520.684
90% confidence interval on the population mean =(450.826, 520.684)
90% prediction interval on the rainfall for the next year =(367.458, 704.516)
The length of 90% prediction interval on the rainfall for the next year is large than the 90% confidence interval on the population mean.
Regression Analysis
r²
0.098
n
20
r
0.313
k
1
Std. Error
88.142
Dep. Var.
rainfall
ANOVA table
Source
SS
df
MS
F
p-value
Regression
15,219.5306
1
15,219.5306
1.96
.1786
Residual
139,841.0589
18
7,768.9477
Total
155,060.5895
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=18)
p-value
90% lower
90% upper
Intercept
435.5232
40.9446
10.637
3.43E-09
364.5227
506.5236
t
4.7840
3.4180
1.400
.1786
-1.1430
10.7110
Predicted values for: rainfall
90% Confidence Interval
90% Prediction Interval
t
Predicted
lower
upper
lower
upper
Leverage
21
535.987
464.986
606.987
367.458
704.516
0.216
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