# Question: question 1 1 mark for the two variables in your...

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Case Study

Life insurance companies are interested in predicting how long their customers will live because

their premiums and protability depend on these numbers. An actuary for one insurance company

gathered data from 100 recently deceased male customers. He recorded the age at death of the

customer plus the ages at death of his mother and father, the mean ages at death of his grandmothers

and the mean age at death of his grandfathers. These data are recorded in columns 1 to 5 respectively

in the data set.

The actuary would like to determine whether the age at death of a customer's mother is useful

in predicting the life expectancy (age at death) of the customer. Use Excel to generate the following

output for the variables age at death of a customer's mother and life expectancy (age at death) of

the customer.

Question 1 (1 mark)

For the two variables in your analysis the dependent variable is

a) age at death of a customers mother

b) age at death for a customers father

c) mean age at death for a customers grandmothers

d) mean age at death for a customers grandfathers

e) age at death of a customer

and the independent variable is

a) age at death of a customers mother

b) age at death for a customers father

c) mean age at death for a customers grandmothers

d) mean age at death for a customers grandfathers

e) age at death of a customer

Question 2 (1 mark)

The correlation coecient (correct to 3 dp) for the two variables: age at death of a customer's mother

and the life expectancy (age at death) of the customer is

Question 3 (1 mark)

The correlation between the two variables: age at death of a customer's mother and the life ex-

pectancy (age at death) of the customer is a

a) very weak

b) weak

c) moderate

d) strong

e) very strong

and

a) positive linear correlation

b) negative linear correlation

Question 4 (1 mark)

The equation of theline which best ts the data in the scatterplot is given by

a) y

b) y hat

answer style: a/b = ? + ?x

Express the regression coecients to 3 dp.

Question 5 (4 marks)

To test for a signicant linear relationship between age at death of a customer's mother and the life

expectancy (age at death) of the customer the appropriate null and alternative hypotheses are

a. Null hypothesis (H0)

a) beta

b) beta sub 0

c) beta sub 1

d) b

e) b sub 0

f) b sub 1

and

a) is less than

b) is more than

c) is equal to

d) is not equal to

and

a) -1.0

b) -0.5

c) 0.0

d) 0.5

e) 1.0

b. Alternative hypothesis (HA)

a) beta

b) beta sub 0

c) beta sub 1

d) b

e) b sub 0

f) b sub 1

and

a) is less than

b) is more than

c) is equal to

d) is not equal to

and

a) -1.0

b) -0.5

c) 0.0

d) 0.5

e) 1.0

c. The p value of the test correct to 5 dp is

d. Should we reject H0? The conclusion will be

There is

a)

b)

evidence at = 0:0100 to conclude that there

a) sufficient

b) insufficient

a significant linear relationship between age at death of a customer's mother and the life expectancy (age at

death) of the customer.