Q1: A study on the occurrence of line faults in an electricity supply network was carried out over a two-year period. Data was collected from six regions on the number of faults per year in each of the two years, and gave the results shown in the table below.
Region Year Line length (miles) # of Faults.
Midlands 2000 15.6 15
Midlands 2001 15.6 18
North 2000 23.66 22
North 2001 23.66 16
South 2000 26.40 23
South 2001 26.40 18
East 2000 33.58 18
East 2001 33.58 28
West 2000 47.30 33
West 2001 47.30 27
Coast 2000 50.64 30
Coast 2001 50.64 27
(a) Does the data indicate that the number of faults per mile has changed from year 2000 to year 2001?
(b) Draw the graph relating Number of Faults to Line length.
(c) Does the data support the suggestion that the two variables (# Faults and Line length) are related? If so, find the relationship between them and state the probable limits of the Regression Coefficient with 95% confidence.
(d) Test the hypothesis that the graph should pass through the origin. Explain what this means in practical terms.