Statistics Exam Worked Solutions — MTN, Mega Brain & Chi-sq

QUESTION 1    (20 MARKS)

• MTN is a telecommunication network company operating in Ghana, Nigeria, Zimbabwe and South Africa. Mr. Ekena Ikechukwu, the new appointed CEO of MTN Nigeria Limited has recently bought a new Lamborghini Urus Super SUV for personal use. The number of miles that a particular car can run before its battery wears out is exponentially distributed with an average of 10,000 miles. The owner of the car needs to take a 5000-mile trip. What is the probability that he will be able to complete the trip without having to replace the car battery?

(10marks)

• The number of minutes between customers who enter a certain shop can be modelled by the exponential distribution. Assuming that a new customer enters a shop every two minutes, on average. After a customer arrives, using the CDF formula, calculate the probability that a new customer arrives in less than one minute.       (10marks)

QUESTION 2          (20 MARKS)

Mega Brain Consult is an auditing firm with branches at Cape Town, East London and Port Elizabeth. The firm core business is to prepare year-end financial statements, auditing, filing VAT and income tax, business advisory, marketing intelligence and research to its clients. Since its establishment in 2019, the firm has made lots of success in terms of customer service, operations, and profitability. However, in recent times, the firm has been experiencing cash flow problems as it has been alleged that the managing has been siphoning the firm’s income. The owner of Mega Brain Consult, Dr Elsie Adoma, has analysed the value of services offered to clients by the firm with the pass 24 months and randomly sampled 25 services that customer offered to customers and the amount each customer paid. After the initial investigation, it was revealed that the sample mean R170, with a sample standard deviation of R22. Based on this scenario,

• Estimate, with 95% confidence, the actual mean value of credit card purchases by all their credit card customers.      (10marks)

• Assume that 46 credit card purchases were sampled. Set 95% confidence limits for the actual mean value of credit card purchases at this home store (σ is unknown).    (10marks)

QUESTION 3           (20 MARKS)

An international study on executive working hours reported that company CEOs (chief executive officers) worked more than 60 hours per week on average. During a statistics class, students were asked to conduct a research to test whether this norm applied to South African CEOs as well. Based on this, students randomly sample 90 South African CEOs and each CEO was asked to record the number of hours worked during a given week. The sample mean

number of hours worked per week was found to be 61.3 hours. Assume a normal distribution for weekly hours worked and a population standard deviation of 8.8 hours.

Test this claim at 5% level of significance that, whether South African CEOs work more than 60 hours per week.                                                                                                                                 (20marks)

QUESTION 4       (20 MARKS)

Dr. Kwarteng Academic Research Centre is investigating into performance of Richfield Cape Town students at the end of year exams. A previous research conducted five years ago before COVID and the follow are the results. First year students recorded 40%, second year students scored 25%, final year students recorded 20%, while higher certificate students recorded 15%. BCom statistics students conducted a recent investigation and sampled 400 Richfield Cape Town students based on their year of study. The study established that following results; first year student recorded 135, second year students recoded 115, third year students recorded 96, while the remainder was recorded by higher certificate students

Can Dr. Kwarteng Academic Research Centre conclude that student performance patterns have changed since the study five years ago? Test the hypothesis at the 5% level of significance. (20marks)

QUESTION 5       (20 MARKS)

Media24 publishes three magazines for the teenage market (male and female readers between 16 and 19 years of age). Assuming further that the executive editor of Media24 would like to answer the following: ‘Are readership preferences for the three magazines independent of gender?’

Based on this, a survey was carried out amongst 200 teenagers (of both genders) in various bookstores. Randomly selected teenagers who bought at least one of the three magazines were interviewed and asked the following question: ‘Which one of these three magazines do you most prefer to read?’ The gender of the respondent was also noted. The magazine preference responses by gender is summarised in Table below:

Cross-tabulation table of gender by magazine preference

Are readership preferences for the three magazines independent of gender? Test, at the 5% level of significance, whether there is a statistical association between gender and magazine preference (i.e. whether or not they are statistically independent).                                          (20marks)

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Statistics Assignment Answers: Expert Answers on Above Questions on Statistics

Exponential life time with mean

μ = 10000 Rate = 1/10000

The probability that the battery last for more than 5000 miles is e−λ(5000) = e−5000/10000

=06065 which is 60.65%

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