Question one

A survey to establish the relationship of salary with degree program done at varsity and type of institution (government department) a graduate is working with was done. Survey results from 45 students who had just worked for one year are presented in the table (in '00US dollars).

Financial

Academic

research

QE

5, 8, 3

4, 2, 4

4, 5, 3

Stat

4, 6, 7

2, 4, 7

2, 4, 8

Actuarial

3, 4, 6

3, 5, 2

4, 6, 3

Bsc

4, 4, 9

2, 1.4, 3

3, 4, 7

BPS

5, 6, 4

3, 2, 2

4, 5, 3

(a)Define ANOVA Model (effects model with interaction) for these data.

(b)Investigate if there was an interaction between type of institution and degree program taken at varsity(include ANOVA table in your answer)

(c)Test the following contrasts;

(i)

(ii)where is the mean of the ith program

Are the contrasts in (c) orthogonal?

(HINT:)

Question two

A manufacturing firm wants to investigate the effects of 5 color additives on the setting time of a new concrete mix. The firm notices that setting times can be affected by a given day's temperature and humidity and they did take temperature and humidity settings are categorized them into 4 levels. The ANOVA table for the data from their experimentation is given in table 1 summary of treatment means

Source dfSSMSF

Additives71.732.8

Temp

Additive*temp393.67

Residual

Total 39782.89

(a)Complete the table(12)

(b)Make conclusions about the general hypotheses of ANOVA(3)

(c)Summarize the findings from this analysis to the researchers(2)

(d)Noting that the study design was balanced, compute LSD atfor comparing interaction means (3)

END