# Probability and statistics question thread (1 Viewer)

#### boredsatan

##### Member
Can someone please verify if my answers are correct for the below questions?

People have one of four different blood types – O, A, B or AB. Suppose 49% of the population have blood type O, 38% have type A, 10% have type B and 3% have type AB.
a) What is the probability that a randomly selected person
i) does not have type O blood? 0.51
ii) has type A or type B blood? 0.48
iii) is neither type O nor type A? 0.13
b) Among 4 random patients, what is the probability that
i) all have type O? (0.49)^4 = 0.05764801
ii) none of them are type A? (0.62)^4 = 0.14776336
iii) at least one person is type B? 1 - ((0.90)^4) = 0.3439
iv) the third patient only is type A? 0.62*0.62*0.38*0.62 = 0.09056464

Suppose a new cancer treatment has a 20% chance of curing a patient
a) For 5 cancer patients, what is the probability that:
i) none will be cured? 5C0 * (0.2)^0 * (0.8)^5 = 0.32768
ii) exactly 2 patients will be cured? 5C2 * (0.2)^2 * (0.8)^3
iii) at least 2 patients will be cured? P(X = 1) = 5C1 * (0.2)^1 * (0.8)^4 = 0.4096
P(X = 0) = 0.32768
P(X >=2) = 1 - (0.32768 + 0.4096) = 0.26272

b) For 500 patients
i) how many would you expect to be cured by the treatment? 500 * 0.20 = 100 patients
ii) what is the probability that more than 75 of the patients are cured?
variance = np(1-p) = (500*0.20)(0.8) = 80
so the standard deviation = sqrt(80)
using normal distribution with mean as 100 and standard deviation as sqrt(80)
P(X > 75) = 0.9974

Thanks!

#### ultra908

##### Active Member
Looks right to me!

#### boredsatan

##### Member
Looks right to me!
So are you 100% sure that all the working out and answers of mine are correct?
Thanks

#### boredsatan

##### Member
Can I please have help with these questions?
2.1 For the following statement about a statistical survey, identify the following items (if possible). If you can’t tell, then say so – this often happens when we hear or read about a survey. A recent online poll conducted by an Australian newspaper of 1083 registered voters found that 43% of the respondents believe it is likely that bushfires are linked to climate change
a) The possible population of interest
b) The population parameter
c) The sampling frame
d) The sample
e) The sampling method, including whether or not randomisation was employed
f) Who (if anyone) was left out of the study
g) Any potential sources of bias you can detect and any problems you see in generalising to the population of interest

2.2 What’s the design? Read the brief description related to a statistical study below, and
a) explain why it is an experiment rather than an observational study
Runners recovering from lower leg fractures were randomly allocated to three different training programs. Half of each group also followed a high calcium diet. Bone density measurements were taken for all subjects.

Also
b) identify the factor(s) in the experiment and the number of levels for each.
c) give the total number of treatments.
d) state the response variable(s) measured
e) explain whether it was blind, or double-blind

2.3 Some studies suggest that having a pet can provide positive mental and physical health benefits for the owner. A particular study involving elderly people who lived alone reported that dog owners had lower blood pressure on average than the non dog-owners, with the difference in average blood pressure between the groups statistically significant.
a) In this context, what does “statistically significant” mean?
b) Explain why this study would be an observational study rather than an experiment.
c) Does this result mean that if an elderly person buys a dog that their blood pressure will decrease? Explain.
d) Suggest some possible associated confounding variables for this study.

Thanks

#### Trebla

Where are these questions coming from? There are concepts in there beyond the HSC syllabus.

#### 5uMath

##### Member
Can I please have help with these questions?
2.1 For the following statement about a statistical survey, identify the following items (if possible). If you can’t tell, then say so – this often happens when we hear or read about a survey. A recent online poll conducted by an Australian newspaper of 1083 registered voters found that 43% of the respondents believe it is likely that bushfires are linked to climate change
a) The possible population of interest
b) The population parameter
c) The sampling frame
d) The sample
e) The sampling method, including whether or not randomisation was employed
f) Who (if anyone) was left out of the study
g) Any potential sources of bias you can detect and any problems you see in generalising to the population of interest

2.2 What’s the design? Read the brief description related to a statistical study below, and
a) explain why it is an experiment rather than an observational study
Runners recovering from lower leg fractures were randomly allocated to three different training programs. Half of each group also followed a high calcium diet. Bone density measurements were taken for all subjects.

Also
b) identify the factor(s) in the experiment and the number of levels for each.
c) give the total number of treatments.
d) state the response variable(s) measured
e) explain whether it was blind, or double-blind

2.3 Some studies suggest that having a pet can provide positive mental and physical health benefits for the owner. A particular study involving elderly people who lived alone reported that dog owners had lower blood pressure on average than the non dog-owners, with the difference in average blood pressure between the groups statistically significant.
a) In this context, what does “statistically significant” mean?
b) Explain why this study would be an observational study rather than an experiment.
c) Does this result mean that if an elderly person buys a dog that their blood pressure will decrease? Explain.
d) Suggest some possible associated confounding variables for this study.

Thanks
I will look at 2.1 and 2.2 later when I have a bit more time.

2.3 a) There is statistical evidence that there is a difference.

b) If it were an experiment, the elderly people would know that this was being undertaken, and the Hawthorne effect would therefore be evident (Hawthorne effect is when a study is taken and the subjects of the study know that they are being studied). This is an observation as there was no formal way of collecting and analysing the data.

c) No. It increases the likelihood of it happening with respect to those particular elders, however the responsibility of a dog could potentially act as a factor which increases blood pressure.

d) Confounding variables are not in the maths syllabus, so don't worry about it if you are just doing these questions. If it is an assignment question, I would say that confounding variables in this particular case (which are variables that impact both independent and dependent variable) could be the dog breed, dog colour, dog's attitude, elder's treatment to the dog and so on.

Hope this helps!

#### ultra908

##### Active Member
Where are these questions coming from? There are concepts in there beyond the HSC syllabus.
idk alot of these qs u could answer using a combination of science and maths HSC knowledge i think.

#### boredsatan

##### Member
Thanks 5uMath for helping me with 2.3
Can I please have help with questions 2.1 and 2.2?
2.1 For the following statement about a statistical survey, identify the following items (if possible). If you can’t tell, then say so – this often happens when we hear or read about a survey. A recent online poll conducted by an Australian newspaper of 1083 registered voters found that 43% of the respondents believe it is likely that bushfires are linked to climate change
a) The possible population of interest
b) The population parameter
c) The sampling frame
d) The sample
e) The sampling method, including whether or not randomisation was employed
f) Who (if anyone) was left out of the study
g) Any potential sources of bias you can detect and any problems you see in generalising to the population of interest

2.2 What’s the design? Read the brief description related to a statistical study below, and
a) explain why it is an experiment rather than an observational study
Runners recovering from lower leg fractures were randomly allocated to three different training programs. Half of each group also followed a high calcium diet. Bone density measurements were taken for all subjects.

Also
b) identify the factor(s) in the experiment and the number of levels for each.
c) give the total number of treatments.
d) state the response variable(s) measured
e) explain whether it was blind, or double-blind

#### boredsatan

##### Member
Can I have help with this question please?
2.5 Weather forecasts are generally right, but not always. For a particular winter, the local forecast predicts rain for 35% of days and rain occurs on 38% of the days. For 25% of winter days, rain was forecast and rain does fall. Hint: Use a Venn diagram to help answer the following questions about rainy days.
a) For what percentage of days does it rain without rain being forecast?
b) What is the probability that there was no rain forecast nor did it rain?
c) On what percentage of days was there either rain or rain forecast?
d) If it is raining, what is the probability that rain was forecast?
e) Are rain and forecast for rain mutually exclusive events? Explain.
f) Are rain and forecast for rain independent events? Explain.

#### boredsatan

##### Member
Can I please have some more help?
For the following statement about a statistical survey, identify the following items (if possible). If you can’t tell,
then say so – this often happens when we hear or read about a survey.
A recent online poll conducted by an Australian newspaper of 1083 registered voters found
that 43% of the respondents believe it is likely that bushfires are linked to climate change

a) The possible population of interest
Registered voters

b) The population parameter
Proportion of registered voters who believe it's likely that bushfires are linked to climate change

c) The sampling frame
Not stated in the question

d) The sample
1083 registered voters

e) The sampling method, including whether or not randomisation was employed
voluntary response sample

f) Who (if anyone) was left out of the study
People who didn't participate in the study

g) Any potential sources of bias you can detect and any problems you see in generalising to the population of
interest
People are more likely to participate in the survey if they have a strong opinion towards either side. What source of bias would this be?

#### mgg20

##### New Member
Can someone please verify if my answers are correct for the below questions?

People have one of four different blood types – O, A, B or AB. Suppose 49% of the population have blood type O, 38% have type A, 10% have type B and 3% have type AB.
a) What is the probability that a randomly selected person
i) does not have type O blood? 0.51
ii) has type A or type B blood? 0.48
iii) is neither type O nor type A? 0.13
b) Among 4 random patients, what is the probability that
i) all have type O? (0.49)^4 = 0.05764801
ii) none of them are type A? (0.62)^4 = 0.14776336
iii) at least one person is type B? 1 - ((0.90)^4) = 0.3439
iv) the third patient only is type A? 0.62*0.62*0.38*0.62 = 0.09056464

Suppose a new cancer treatment has a 20% chance of curing a patient
a) For 5 cancer patients, what is the probability that:
i) none will be cured? 5C0 * (0.2)^0 * (0.8)^5 = 0.32768
ii) exactly 2 patients will be cured? 5C2 * (0.2)^2 * (0.8)^3
iii) at least 2 patients will be cured? P(X = 1) = 5C1 * (0.2)^1 * (0.8)^4 = 0.4096
P(X = 0) = 0.32768
P(X >=2) = 1 - (0.32768 + 0.4096) = 0.26272

b) For 500 patients
i) how many would you expect to be cured by the treatment? 500 * 0.20 = 100 patients
ii) what is the probability that more than 75 of the patients are cured?
variance = np(1-p) = (500*0.20)(0.8) = 80
so the standard deviation = sqrt(80)
using normal distribution with mean as 100 and standard deviation as sqrt(80)
P(X > 75) = 0.9974

Thanks!
Hi,
I am also answering this question but I was wondering what ^ refers to?
I just struggling to understand what I am suppose to do to find the answer
Thanks

#### boredsatan

##### Member
Hi,
I am also answering this question but I was wondering what ^ refers to?
I just struggling to understand what I am suppose to do to find the answer
Thanks
it means raised to
for exam 2^3 means 2 raised raised to the power of 3, or you could also say 2 cubed

#### mgg20

##### New Member
Did anyone find the answers for this? I am also struggling with this question

#### NotMyCabbages

##### New Member
Can I have help with this question please?
2.5 Weather forecasts are generally right, but not always. For a particular winter, the local forecast predicts rain for 35% of days and rain occurs on 38% of the days. For 25% of winter days, rain was forecast and rain does fall. Hint: Use a Venn diagram to help answer the following questions about rainy days.
a) For what percentage of days does it rain without rain being forecast?
b) What is the probability that there was no rain forecast nor did it rain?
c) On what percentage of days was there either rain or rain forecast?
d) If it is raining, what is the probability that rain was forecast?
e) Are rain and forecast for rain mutually exclusive events? Explain.
f) Are rain and forecast for rain independent events? Explain.
Why even do the assignment yourself if you can get others to do it for you

#### boredsatan

##### Member
How do we know when to use pooled vs unpooled?? for hypothesis test

#### Velocifire

##### Out of Order
Wow, I must be special. I have AB-

That means I can life leech all of you!