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STAT131 W9L2 Review Test Paper 2002

STAT131 W9L2 Review Test Paper 2002. by Anne Porter alp@uow.edu.au. Relax, Close your eyes.

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STAT131 W9L2 Review Test Paper 2002

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  1. STAT131W9L2 Review Test Paper 2002 by Anne Porter alp@uow.edu.au

  2. Relax, Close your eyes • The start of this lecture involves closing ones eyes and thinking of some relaxing music, a quiet place and when in this comfort zone to begin to confront the accumulation of formulae and language that has occurred over the past few weeks. Now waken to...

  3. The student’s nightmare

  4. Making Sense of Formulae • To make sense of the formulae and language encountered we need to organise it. When exploring samples of data and developing models for the random variables, whether discrete or continuous, we have sought to identify: • shape (including the probability of some event), • centre (mean, median), • spread (variance and standard deviation) and • fit of models to data (including outliers).

  5. Map your concepts • See if you can organise the various formulae into related groups, attaching words to the symbols as you do so. You may also like to include those formulae which I have ommited. There is a symbolic language to learn in order to give voice to our statistical ideas.

  6. Frame formulae

  7. Maybe some concept maps!

  8. Summary • Maps • Frames • Worked solutions • Interpretations of printout • Interpretations of statistics • Assumptions

  9. Now let us do a past midterm!

  10. Q1: Describing Data Four main features • Outliers one male (2200) None for females • Shape females reasonably symmetric (third quartile narrow) males skewed with longer tail to low numbers • Centre - medians about 2010 • Spread Male IQR about twice female IQR, range for males wider than female

  11. Q2: Poisson • The number of questions posted to the STAT131 forum follow a Poisson distribution at the rate of 3.3 per day. Var(X)= s2 =lt=3.3x1=3.3 Standard deviation(X) = s P(X=0)= P(Y>1) =P(X=0)

  12. Data centred about 3.3 Q2 vi) use of time series to test assumption of constant probability • What does this reveal about the suitability of the Poisson(3.3) distribution • Lack of trend suggests • constant probability • Smoothing (running means • or medians can help smooth)

  13. Q3 Probability • (i) P(Australian)= • (ii) P(Yes )= 110 120 100 330 150 180 110 /330 150/330

  14. Q3 Probability • (iii) P(Yes|Other Nationality)= • (iv) P(Yes and Other Nationality)= 110 120 100 330 150 180 50 yes /100 other nationalities 50/330

  15. Q3 Independence • (v) From looking at the data does it appear that the response is independent of nationality. Yes / No. Explain your answer. 110 120 100 330 150 180 No they are not independent the patterns or responses are different for different nationalities. Knowing nationality helps knowing the probability of agreeing or not

  16. Q3 Independence 110 120 100 330 • (v) From looking at the data does it appear that the response is independent of nationality. 150 180 No they are not independent P(A)xP(B) ≠ P(A and B). P(Australian)=110/330 P(Yes)=150/330 P(Australian & Yes)=20/330 Knowing nationality helps knowing the probability of agreeing or not

  17. Q4: Discrete Random Variables E(X) • The number of passengers packages being mislaid (X) per week is defined by the following probabilities and outcomes 40 30 100 (i)Complete the table (ii)What is E(X) ? =0x0.3+1x0.4+2x0.3=1

  18. Hence Q4: Discrete Random Variables • The number of passengers packages being mislaid (X) per week is defined by the following probabilities and outcomes 40 30 100 X2 0 1 4 E(X)=1 (iii)What is the standard deviation of X? We need x2 Where Var(X)=s2= E(X2)-(E(X))2 Var(X)=1.6-12

  19. 40 30 100 freq 50 40 30 20 10 0 Observed Expected 0 1 2 x Q4: Discrete Random Variables - Graphical Fit • Sketch an appropriate graph to assess goodness of fit. • Do the data seem to fit the model There appears to be a lack of fit as seen by the discrepancy in columns

  20. 40 30 100 Q4: Discrete Random Variables - Chi-square goodness of fit • Use chi-square goodness of fit test to see if the data fit the model =26.6

  21. 40 30 100 Q4: Discrete Random Variables - Chi-square goodness of fit • Use chi-square goodness of fit test to see if the data fit the model Then there is lack of fit If Conclusion As 26.6 >3.828 there is evidence that the data do not fit the model

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