Question 1
There are three insurance companies in the Business
District in Accra. It is known from previous records that
each year, 2 percent, 5 percent and 3 percent of those
insured by Vanguard Insurance, Enterprise Insurance and
Star insurance respectively submit claims. 20 percent of the
people in the community have an insurance policy with
Vanguard Insurance Company, 30 percent with Enterprise
Insurance Company and 50 percent with Star Insurance
Company.
(i) What is the probability that a randomly selected
insurance policyholder in the community did a claim in a
certain year?
(ii) If a randomly selected policy holder in the community
is found to have made a claim in a certain year, what is the
probability that, that person is insured with Vanguard
Insurance?
(iii) If a randomly selected policy holder in the community
is found to have made a claim in a certain year, what is the
probability that, that person is insured with Enterprise
Insurance?
Question 2
(a). Researchers are concerned about the impact of students
working while they are enrolled in classes, and they’d like to know
if students work too much and therefore are spending less time on
their classes than they should be. First, the researchers need to find
out, on average, how many hours a week students are working. EV(6 marks)
3
They know from previous studies that the standard deviation of this
variable is about 5 hours.
(i) A survey of 200 students provides a sample mean of 7.10
hours worked. 95% confidence interval based on this sample is
6.41 to 7.79.
Do you agreed with the researcher that the 95% confident interval of
the unknown population mean of the students worked hours lies
between 6.41 and 7.79?
Indicate whether the researchers are right or wrong, giving reasons
for your answer.
(ii) Based on your understanding of confident interval estimation;
explain the reason why the researcher did not use 100% confidence
level, but instead he used 95% confidence level.
(iii) The researchers are not satisfied with their confidence interval
and want to do another study to find a shorter confidence interval.
What should they change to ensure they find a shorter confidence
interval?
Question 3
The average lifespan of a Ghanaian is 57years. The average
lifespan of males in Ghana is known to be 55 years while the
average lifespan of females in Ghana is known to be 60 years. The
average lifespan of people from the Northern region of Ghana is
known to be 58 years while the average lifespan of people in the
East region of Ghana is known to be 54 years.
Use the above information to answer the following questions:
(i).With your reasons, discuss all possible population parameters
from the above information.
(ii).With your reasons, discuss all possible sample statistics from the
above information.
(iii) Compare and contrast the average lifespan of males and 4
females. Which group average is more likely to represent the
corresponding population parameter? Give reasons for your answer.
Question 4
In each of the following research situations below, determine
whether the data should be analyzed with a parametric test, a
nonparametric test, or both. Give reasons for your answer in each
situation.
(i). You want to compare males and females scores obtained from
an aptitude test where scores on the aptitude test range
between 0 and 100.
(ii). You want to find out whether or not basketball players are
taller than the general population.
(iii). You want to find out whether or not a difference exists
between males and females in their like or dislike for statistics.
(iv). You want to find out among a sample of eligible voters in the
Ghanaian population, whether the political party they voted for in
the 2016 general elections was the same as the political party they
voted for in the 2012 general elections.
(v).You want to compare two groups of university students on their
levels of intelligence, where intelligence scores could range between
30 and 150
Answers
Given : each year, 2 percent, 5 percent and 3 percent of those insured by Vanguard Insurance, Enterprise Insurance and Star insurance respectively submit claims.
20 percent of the people in the community have an insurance policy with
Vanguard Insurance Company, 30 percent with Enterprise Insurance Company and 50 percent with Star Insurance Company.
To Find : What is the probability that a randomly selected insurance policyholder in the community did a claim in a certain year?
(ii) If a randomly selected policy holder in the community is found to have made a claim in a certain year, what is the probability that, that person is insured with Vanguard Insurance?
(iii) If a randomly selected policy holder in the community is found to have made a claim in a certain year, what is the probability that, that person is insured with Enterprise Insurance?
Solution:
Vanguard Insurance, claim = 2 % = 0.02
people in the community Vanguard Insurance = 20% = 0.2
Claim in Vanguard Insurance = (0.02)(0.2) = 0.004 = 0.4 %
Enterprise Insurance, claim = 5 % = 0.05
people in the community Enterprise Insurance = 30% = 0.3
Claim in Enterprise Insurance = (0.05)(0.3) = 0.015 =1.5 %
Star Insurance, claim = 3 % = 0.03
people in the community Star insurance = 50% = 0.5
Claim in Star insurance = (0.03)(0.5) = 0.015 = 1.5 %
probability that a randomly selected insurance policyholder in the community did a claim in a certain year = 0.004 + 0.015 + 0.015
= 0.034 = 3.4 %
if claim then probability that, person is insured with Vanguard Insurance
= 0.004/0/034
= 4/34
= 2/17
= 0.1176
= 11.76%
if claim then probability that, person is insured with Enterprise Insurance
= 0.015/0.034
= 15/34
= 0.4412
= 44.12 %
Please post Questions one by one
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