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Numerical Answers (click the questions for workings/explanation)

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Question 7:

Question 8:

Question 9:

Question 10:

(i)

Using R-formula, , where .

(ii)

Largest value of .

Let

.

(i)

Number of ways ways

(ii)

Number of ways ways

(iii)

Number of ways ways

(i)

The production manager should use a 2 tailed test as he is only interested to test whether there is a difference in the average time taken.

(ii)

The production manager is able to carry out a hypothesis test as the sample average time taken to manufacture the control panels follows an approximate normal distribution by Central Limit Theorem with a sample size larger than 30.

(iii)

unbiased estimate of population mean

unbiased estimate of population variance

Let be the population mean time taken to manufacture a control panel using the alternative process.

Test

against at level of significance.

Under , by central limit theorem, approximately.

Using GC,

Since , we do not reject and conclude that there is insufficient evidence at level of significance that the alternative process will give a different average manufacture time of a control panel.

(iv)

The alternative process may produce control panels of a better quality.

### Relevant materials

MF26

### KS Comments

The specimen paper 2 was useful to provide us with a glimpse of what is to be expected of the upcoming syllabus. The DRV question and binomial question briefly showed us that we need to explore more applications of statistics. It is definitely different from the old 9740 H2 Mathematics Syllabus as the questions are more intuitive and seek to push students’ imaginations more.