Business Statistics

Academic Session 2022
MAY 2022 Semester
ASSIGNMENT
BBM203/03 Business Statistics
INSTRUCTIONS TO CANDIDATES:
1. This assignment is the final assessment to replace the proctored examination.
2. This assignment consists of four (4) questions. Answer ALL questions
3. You are allowed a maximum of one (1) attempt to submit your assignment.
4. The assignment will be made available from 11th July 2022, Monday (00:00) until 1st
August 2022, Monday (23:59).
5. Completed assignment must be submitted by 1
st August 2022, Monday (23:59).
Copyright © 2022 WOU
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 σ
2
, 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)