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Assignment 2 MAS183 ! 1a)! Has HIV? Test Result

Yes

No

Total

Positive

0.049

0.038

0.087

Negative

0.001

0.912

0.913

0.05

0.95

1

Total

b) P (Has HIV I Diagnosed as Postive ) = 0.049/ 0.087 = 0.56322 ≈0.563 (3 dp)! c) P (Does’t have HIV I Diagnosed as Negative ) = 0.912/0.913 = 0.99890 ≈ 0.999 (3dp) ! d) The diagnostic test is better at showing who doesn’t have HIV, as 99.9%( of those who receive negative test results actually don’t have HIV. While out of those who received positive results, only 56.3%(0.049/0.0 87) of them actually have HIV. Therefore, if given a positive result, further tests have to be carried out. ! 2. No it wouldn’t follow a binomial distribution as binomial conditions aren’t met. For example, each trial does not have the same probability of ‘success’ ( there are two options in or out, but none of either is a definite ‘success’, its not clear. It should be go in or doesn’t go in- then going in can be defined as a success) The trials may also not be independent of each other as someone who goes through the entry may have to use it again to leave after, therefore being dependent.! 3a) X= Number of subjects who can’t taste PTC ! All conditions met, therefore binomial distribution. ! ! Probability distribution:! X ~ Bin (20,0.3) ! b) i) µ=20 x 0.3 ! =6! σ= √np(1-p) ! =√20 x 0.3(0.7)! =√4.2 ! =2.04939! ≈2.049 (3dp)! ii) P(x>7)= 1- (Px≤7) ! = 1-0.7723 (value from tables and formulae book)! = 0.2277! iii) P(5≤X≤10)= P(X≤10)-P(X≤4)! =0.9829-0.2375! =0.7454 ! c) It would be unusual as the probability of only one of the subjects not being able to taste PTC (Px=1) is 0.068. This is lesser than 1% which is a very small chance therefore it is very unusual that this event would occur.!

4a) P(265< x 290) = P( z > 290-274.3/8.9) ! = P( z > 1.764044944)! = 1- P( z > 1.764044944)! = 1- P( z > 1.76)! = 1- 0.9608! =0.0392! c) Y~N (µ=274.3, σ=8.9)! In distribution graph, two tails of 0.25 ! Closest P= 0.2514! Z score= -0.67 ! 274.3 ± 0.67 x 8.9 = 274.3 ± 5.963! Lower Quartile (Q1)= 274.3-5.963 ! =268.337! Upper quartile (Q3)= 274.3+5.963! =280.263 5a)i) Bias towards those who have access to a phone as if someone doesn’t they wouldn’t be able to vote on the poll. Also biased towards those who watch that particular news bulletin at that particular time, as for example, it may be playing during weekdays and usually most working class people are out working (and unable to watch TV), therefore removing their input from poll results. That particular news bulletin may also be catered towards a certain audience. ! ! ii) The survey has not been sampled randomly, and therefore has many aspects of bias. Certain groups of people are more likely to respond than others, therefore influencing the results collected. Sample collected wouldn’t represent the population as a whole. ! b)i) Not representative of Murdoch University students as courses may impact ones view on climate change. For example, most MAS183 students may be in a science related field, therefore have a tendency to be more informed and involved in such topics so results may be biased. !

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ii) Representative of Murdoch University students as the units someone does not influence what phone they have. However ,it also can be viewed as not representative as only one aspect of murdoch university students are represented, students from different faculties should be surveyed to provide more reliable data instead of just focusing on one group of people.!...