ETX1100

Tutorial 11
A11.1
Data on manatee deaths due to powerboats was used to construct a linear regression model relating these deaths to the number of registered powerboats. Year
1977
1978
1979
1980
1981
1982
1983

Power boats (thousands)
447
460
481
498
513
512
526

Manatee
Deaths
13
21
24
16
24
20
15

Year
1984
1985
1986
1987
1988
1989
1990

Power boats (thousands)
559
585
614
645
675
711
719

Manatee
Deaths
34
33
33
39
43
50
47

The model obtained was
ˆ
y = −41.43 + 0.1249 x
ˆ
where y is the estimated number of powerboat-related deaths

when the number of registered powerboats in Florida in thousands is
x.
In 1998 there were 914,535 powerboats registered in Florida. (I have been unable to find the number of registrations for other years since
1990.)
According to the model, how many deaths attributable to powerboats would you expect in 1998?

1

In fact, in 1998 in Florida there were 66 manatee deaths attributable to watercraft, while in 1999 there were 82. (See http://www.savethemanatee.org/newsprrecorddeaths.htm.) Comment on these numbers in relation to your calculation.
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A11.2
If a contingency table has 5 row categories and 6 column categories,
(a) How many degrees of freedom are there for the χ 2 test for independence?

(b) What is the critical value for the test of independence for the categories represented in the table at the 1% level of