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Question 1 Explain the following concepts: (a) Confidence leves (2 marks) (b) Qualitative data (2 marks) (c) Multiplication rule (3 marks) (d) Bayes’ Law (3 marks) Question 2 David set a mathematics quiz for his students. The quiz is marked out of 10. His students’ marks are summarized in the table below: Marks Number of students

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Question 1

Explain the following concepts:

(a) Confidence leves (2 marks)

(b) Qualitative data (2 marks)

(c) Multiplication rule (3 marks)

(d) Bayes’ Law (3 marks)

Question 2

David set a mathematics quiz for his students. The quiz is marked out of 10. His students’ marks are summarized in the table below:

Marks Number of students

2 5

3 6

4 4

5 1

6 15

7 20

8 10

9 3

(a) Construct an appropriate frequency table and draw a histogram to depict the data above (10 marks)

(b) Compute the mean (10 marks)

(c) Calculate the variance and standard deviation (10 marks)

(d) Calculate the coefficient of variation (5 marks)

(e) Interpret the distribution of marks as shown in your histogram (5 marks)

Question 3

Part 1

A researcher collected a sample of 50 respondents in a shopping mall on a weekend. The data are organised in the table below:

Respondent University graduate Non-graduate Total
A: Smoker 14 26 40
B: Non smoker 6 4 10
Total 20 30 50

Calculate the following probabilities

(i) Prob (A) (2 marks)

(ii) Prob (University graduate) (2 marks)

(iii) Prob (A University graduate) (3 marks)

(iv) Prob (University graduate A) (3 marks)

Part 2

The random variable Y follows a normal distribution with mean µ and variance σ2 , i.e. Y N(µ, σ2).
Suppose we have the following information:

P(X ≤ 66) = 0.0421 and P(X ≥ 81) = 0.1298

(a) Compute the value of σ = 5 (10 marks)
(c) Calculate P(65 ≤ X ≤ 74) (10 marks)

Question 4

(a) A sample of test scores is obtained. The scores are displayed as follows: 11, 16, 19, 15, 7, 8, 10

Test the hypothesis that the mean score is 15 at 1% significance level (10 marks).

(b) A chemical manufacturer is concerned about the degree of contamination in the raw material shipments purchased from a supplier. Taking a random sample of 20 shipments of raw materials, the standard deviation of contamination is 3.59. Construct the 95% confidence interval for population variance (10 marks)