Question 1 Explain the following concepts:

(a) Parameter (1 marks)

(b) Stratified random sampling (3 marks)

(c) Descriptive statistics (3 marks)

(d) Inferential statistics (3 marks)

Question 2

The following table displays data on height of students (measured in centimeters) in a Business Statistics class. The sample size consists of 30 randomly selected students for a particular class.

Refer to table in question 2 in file

(a) Draw a histogram to depict the data above (5 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 heights as shown in your histogram (5 marks)

Question 3

Part 1: Two fair dice are rolled

(a) Calculate the probability that two sixes will appear? (2 marks)

(b) Calculate the probability of at least one six appearing? (5 marks)

Part 2

(a) A bank conducted a survey to estimate the proportion of its customers who would be interested in using a new app for mobile banking services. The bank found that 68 out of 150 customers are in favour of using the new app. Construct a

(i) 95% confidence interval (10 marks)

(ii) 90% confidence interval (10 marks)

For the proportion of customers who are in favour of the new banking app

(b) A certain security system contains 12 parts. Suppose that the probability that each individual part will fail is 0.3 and that the parts fail independently of each other. Given that at least two of the parts have failed, compute the probability that at least three of the parts have failed? (8 marks)

Question 4

(a) The mean lifetime of 200 mobile phones in a sample is 1,000 hours and their standard deviation is 130 hours. µ is the mean lifetime of all the mobile phones produced. Test the hypothesis that the sample comes from a population whose mean is 1,200 hours at 1% significance level? (10 marks)

(b) Consider a random sample of 20 observations. The sample variance is 30.5. Construct a 95% confidence interval for σ 2 (10 marks)

BBM 203/03 BUSINESS STATISTICS Semester May 2022

ASSIGNMENT 1

Instructions:

1. Answer ALL questions. 2. Your answers should be typed in A4-sized paper 3. Handwritten assignments will not be accepted 4. This is an individual assignment 5. There will be no Turnitin for this assignment BUT that does not mean you

can copy from your course mates 6. You should use Arial font for your assignment. Font size shall be 12 and

double-spaced. 7. All students must submit the T-DF Assignment Declaration Form as the

front cover when you submit your assignment. 8. Please submit the assignment by 11.59pm, 2 July 2022

Question 1

Explain the following concepts:

(a) Parameter (1 marks) (b) Stratified random sampling (3 marks) (c) Descriptive statistics (3 marks) (d) Inferential statistics (3 marks)

Question 2

The following table displays data on height of students (measured in centimeters) in a Business Statistics class. The sample size consists of 30 randomly selected students for a particular class.

Height (m) Students

140 ≤ y < 145 5 145 ≤ y < 150 6

150 ≤ y < 155 1 155 ≤ y < 160 2

160 ≤ y < 165 10 165 ≤ y < 170 3

170 ≤ y < 175 2

175 ≤ y 1

(a) Draw a histogram to depict the data above (5 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 heights as shown in your histogram (5 marks)

Question 3

Part 1: Two fair dice are rolled

(a) Calculate the probability that two sixes will appear? (2 marks) (b) Calculate the probability of at least one six appearing? (5 marks)

Part 2

(a) A bank conducted a survey to estimate the proportion of its customers who would be interested in using a new app for mobile banking services. The bank found that 68 out of 150 customers are in favour of using the new app. Construct a (i) 95% confidence interval (10 marks) (ii) 90% confidence interval (10 marks)

For the proportion of customers who are in favour of the new banking app.

(b) A certain security system contains 12 parts. Suppose that the probability that each individual part will fail is 0.3 and that the parts fail independently of each other. Given that at least two of the parts have failed, compute the probability that at least three of the parts have failed? (8 marks)

Question 4

(a) The mean lifetime of 200 mobile phones in a sample is 1,000 hours and their standard deviation is 130 hours. µ is the mean lifetime of all the mobile phones produced. Test the hypothesis that the sample comes from a population whose mean is 1,200 hours at 1% significance level? (10 marks)

(b) Consider a random sample of 20 observations. The sample variance is 30.5. Construct a 95% confidence interval for σ2 (10 marks)

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May 29, 2023

May 29, 2023