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MAST10010 Data Analysis 1

Semester 2, 2021

Question 1 (12 marks)

Exploring Potassium oxide — K2O [2 + 4 + 4 + 2 = 12 marks]

Produce on-screen Descriptive Statistics for Potassium oxide concentration (K20) and complete the following table:

N	Mean	StDev	Minimum	Q1	Median	Q3	Maximum	IQR
122

Produce a dotplot and boxplot of K2O on-screen (do not copy onto your test paper). Describe the distribution of Potassium oxide concentration commenting on any unusual features. In particular comment on the glass specimens with Potassium oxide concen- tration higher than 0.85%. What, if anything, do they have in common?

(c) Use Minitab to produce a 95% CI for the mean of K2O. Record the relevant table value, standard error and hence the 95% CI in the spaces provided below; also interpret your conﬁdence interval in the context of the data.

Table value:

Standard error:

95% CI for mean Potassium oxide concentration, µK2O:

Interpret your CI in the context of the data:

(d)

To produce this CI you made two important assumptions. Specify these assumptions and comment on whether they are satisﬁed. Support your comments by referring to a graphical display produced (on-screen only) in Minitab and citing any relevant statistics.

Question 2 (12 marks)

Does glass from di↵erent locations have di↵erent Silica (SiO2) concentrations? [2 + 2 + 2 + 1 + 2 + 3 = 12 marks]

(a) To begin investigating this question produce, on-screen, an appropriate one-way analysis

of variance table and complete the table below.

Source	DF	Adj SS	Adj MS	F-value	P-value
Location					0.000
Error			1.579
Total	121	413.8

Specify (in words) the two models being compared in the ANOVA table.

For each model, give a measure of how well the model ﬁts the data.

State the hypotheses (in terms of the parameters being tested).

Give the conclusion of the ANOVA test, in the context of the data.

Use a further (comparative) analysis to draw a diagram showing which means are sig- niﬁcantly di↵erent. Include a statement about the level of conﬁdence you have in these conclusions. Comment on the di↵erence in mean Silica concentration for the di↵erent locations: in particular, how many di↵erent groups do you think are represented in this sample?

Diagram:

Comment:

Question 3 (12 marks)

Exploring the relationship between Barium oxide and Titanium oxide [3 + 1 + 1 + 2 + 3 + 2 = 12 marks]

(a) Produce on-screen a scatterplot of Barium oxide (BaO) by Titanium oxide (TiO2).

Comment on the relationship between Barium oxide and Titanium oxide.

(b) Give the equation of the line of best ﬁt.

(d) Predict, with 95% conﬁdence, the expected Barium oxide for a specimen of glass with Titanium oxide = 0.18%. Record your prediction interval in the space below. Also, state which location(s) this specimen of glass, with Titanium oxide = 0.18%, is most likely to have come from.

Interval:

Location(s):

(e) Minitab identiﬁed some points as being‘Unusual Observations’. Circle three of these

points on the graph below. Do you expect these values to impact upon the quality of predictions for Barium oxide based on this model? If so, how? Explain.

(f) Produce on-screen a scatterplot “With Regression and Groups”that shows the rela-

tionship between BaO and TiO2 for the di↵erent locations. Comment on the e↵ect of

Location on the relationship between BaO and TiO2.

Question 4 (2 marks)

Summing Up [2 marks] The archaeologists who analysed these data categorised the glass into three groups as follows:

Glass found at Locations 1 and 2 were produced at a single site;