MAS284: Applied Statistics and Process Management

External Assignment 4

Internal assignment 3

Due: Wednesday, May 23.

Semester 1, 2012

Where appropriate, you may use MINITAB/EXCEL or any suitable statistical package; not

all questions will need the use of a statistical package. Should you use a statistical package,

you should cut and paste the relevant part of the output next to your answer. If you hand

in an unedited output, it should be annotated and be placed immediately before or after your

comments/answers to the question; outputs placed as ‘appendices’ or not properly identiﬁed

may not be marked.

The data for question 1, 2 and 4 can be found in the MINITAB/EXCEL ﬁle

a4 2012.MTW/a4 2012.xlxs in LMS.

1.

(14 marks)

Monthly loan applications for a local bank over a three years period were as follows: (read

across from left to right):

20 22 26 30 36 35 40 41 36 32 34 22

19 19 22 30 31 30 36 39 37 36 36 32

29 30 28 32 38 37 39 44 48 47 33 28

(a) Graph the time series and identify any distinctive features of the plot.

(b) (i) Fit a linear trend line to the data.

(ii) Is the trend line signiﬁcant? Justify.

(iii) Explain brieﬂy the reasons for the signiﬁcance or non-signiﬁcance of the trend

line and the small R

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value?

(c) An AR(3) model is ﬁtted to the loan data with the results given below. Based on

these results, would it be reasonable to ﬁt a smaller order autoregressive model?

Justify.

Final Estimates of Parameters

Type Coef SE Coef T P

AR 1 1.3677 0.1738 7.87 0.000

AR 2 -0.4707 0.2996 -1.57 0.126

AR 3 0.1007 0.2094 0.48 0.634

Number of observations: 36

Residuals: SS = 697.749 (backforecasts excluded)

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MS = 21.144 DF = 33

2.

(12 marks)

In a random sample of 33 junior executives, each is classiﬁed by potential for promotion

as good, poor, or uncertain. Each is given a test to measure his or her level of anxiety.

The coded results (the higher the value the higher the level of anxiety) are as follows:

Good 4 5 4 3 2 5 3 2 5 4 4 4 3

Poor 4 8 7 5 5 4 9 9 6 7

Uncertain 5 4 7 4 7 5 4 5 3 5

What are your conclusions about this study? Write a brief report which should include

the appropriate hypotheses and an evaluation of assumptions.

3. (12 marks)

Suppose that a golf association wants to compare the mean distances travelled by four

diﬀerent brands (A, B, C and D) of golf balls when struck with a driver. A randomised

block design is employed utilising a random sample of 8 golfers, with each golfer using a

driver to hit four balls one from each brand in a random order. The distance travelled is

to be recorded for each hit.

(a)

Why is a randomised block design employed and why is randomisation necessary?

(b) The experiment was carried out as designed but the results were erroneously analysed

as if the experiment had been completely randomized (i.e. no blocking) with the oneway

ANOVA output given below. Based on this output, is there evidence that the

mean distances associated with the brands diﬀer?

(c)

Suppose the sum of squares due to the golfers is 4264. Set up the ANOVA table that

will incorporate this information. Is the conclusion the same as that in (b)?

Analysis of Variance for dist

Source DF SS MS F P

brand 3 2652 884 2.51 0.079

Error 28 9832 351

Total 31 12484

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4. (12 marks)

The temperature and pressure used in molding a certain plastic aﬀect its tensile strength.

The following table show the tensile strength (coded) of specimens of plastic molded at 3

diﬀerent temperatures (coded 1,2,3) and under 3 diﬀerent pressures (coded A,B,C).

pressure

temperature A B C

10 10 8

1 11 10 8

12 9 8

12 8 9

8 12 9

2 9 12 8

9 11 9

8 11 9

8 9 10

3 9 9 10

9 10 11

9 9 11

(a) Calculate the means for the four observations in each temperature-pressure group.

Plot the means of the nine groups on a graph with tensile strength on the y axis and

temperature on the x axis. For each pressure, connect the three points corresponding

to the diﬀerent temperatures. What does the plot tell you regarding interaction and

main eﬀects? [ Note that you can alternatively plot the nine points on a strength vs

pressure graph and for each temperature, connect the three points corresponding to

the diﬀerent pressures.]

(b)

Run a two-way ANOVA on these data. Summarize the results of the signiﬁcance

tests.

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