Problem Solving in Statistics and Probability

PROBLEM SOLVING
TASK 2
SIT191
Student Name
[Pick the date]

2.1
Population have blood type O = 49%
Population have blood type A = 38%
Population have blood type B = 10%
Population have blood type AB = 3%
(a) Random sampling is considered the suitable technique to represent the different blood groups.
Blood group O 0 – 48
Blood group A 49 – 86
Blood group B 87 – 96
Blood group AB 97 – 99
(b) Simulation to calculate the number of donors required to ensure that that at least three
people with O blood group and one person with A blood group
Minimum four person needs to be involved for the simulation trial.
Final estimate would be calculated as shown below.
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Therefore, it can be concluded that approximately 8 donors are required to ensure that that at
least three people with O blood group and one person with A blood group.
2.2
a) The population would consist of the residents in a particular city.
b) Proportion of Australians who tend to consume some kind of multivitamins on a daily basis.
c) All the residents that reside in that city
d) Shopper at the local supermarket
e) Randomisation was not observed in the sample since only shoppers from the local
supermarket were used for survey
f) People who do not shop from supermarkets; people those who tend to shop from other
supermarkets or people those who cannot afford shopping from supermarket would be excluded
in the survey.
g) With regards to multivitamin consumption, it is quite possible that the underlying
consumption pattern of those shoppers visiting the supermarket might be different from those
who do not visit supermarket.
2.3
a) The given study would be classified as experimental and not observation since the underlying
treatment is controlled by the researcher. This is apparent since 50% of the volunteers who
participated were given trial drug while the remaining was given placebo.
b) The people suffering from breast cancer are the subjects studied.
c) The underlying factor is the trial drug with two levels being drug received and placebo
received.
d) There are two treatments in the given experiment namely receiving the trial drug and
receiving the placebo.
e) The response variable is the healing of patient suffering from breast cancer.
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f) The design is completely randomised since the researchers are not aware of the treatments
received by a given volunteer.
g) The experiment is double blind since neither the researchers nor the volunteers are aware as to
whether they are receiving the trial drug or the placebo.
h) The given experiment would allow us to understand the healing capacity of the trial drug with
regards to breast cancer patients.
2.4
a) For the given context, statistically significant means that for the given level of there is
difference in the fitness level of people who are regular dancers and those who do not dance at
all.
b) The given study is observational since the people are selected according to whether they dance
regularly or do not dance. No treatment has been given to the participants and instead the fitness
levels are observed.
c) It is imperative to note that dancing does not lead to fitness. However, it has been observed
that people engaged in dancing on a regular basis on average are more fit in comparison to
people those who do not dance at all. It is quite possible that fitness level of a person not engaged
in regular dance could be high but the proportion of such people would be less.
d) Yes, an experiment can be designed for possible link between dancing and fitness. In such a
study, there would be two treatments namely regularly dancing and no dance at all.
2.5
Probability calculation
Let’s defined the variables
C = Chicken
B =Beef
A =Bacon
F =Fish
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