HM6007 Statistics for Managers Assignment Sample

HM6007 Statistics for Managers Assignment

Question 1 (10 marks)

A. Probabilities measure the likelihood of the occurrence of events, and in practice, there are different methods to assign probabilities.

i. Based on the content you learned in in this unit, discuss the main methods used to assign probabilities.

The main methods of probability assignment are the classical, relative-frequency , and subjective categories. The classical method uses the equally likely outcome approach where probability is the number of favorable outcomes to number of outcomes possible (Bello, et. al., 2023, p2(2)). Relative frequency approach of probability entails the use of the probability of occurrence of an event in subsequent tries. A subjective method involves the use of a person’s opinion based on their knowledge or feeling in the case of scant information or no statistics. All of them contemplate likelihood from a different angle, into meeting different situations and with different levels of information given.

ii. In real-world decision-making, can we rely on any single method, or do they vary based on the situation for which we need to assign probabilities? Justify your answer.

In practical application, the use of these methods with regard to probabilities would be unfeasible; the method to be used depends on the circumstances. The classical method for MBA assignment expert is applicable when the decisions are obvious such as events with probability that is equal and known. Relative frequency approach works well when there is past data that is sufficient, a common example is with the quality control. The process of calculating profitability involves two stages where the first is the subjective method, which is important for the absence of significant material in many cases, it reveals with the help of expert assessment, for example in the prognosis of low-frequency events. Integrating approaches or modifying them to the specifics of certain applications makes the assessments and estimations more precise and definitive, thus offering a better appreciation of probabilities in a wide variety of decision-making situations.

B. Urban Insight Research requires expert advice on selecting optimal sampling plans for their data collection initiatives in the following research scenarios.

Scenario

1. A research to review the public sentiment regarding COVID-19 annual booster vaccination.

2. A research to assess the socioeconomic status of residents in rural areas of Victoria, Australia.

Required:

For each scenario, you are required to:

i. Discuss at least two alternative sampling methods,

ii. Explain the significance of each method in the context of the research,

iii. Describe the sampling process using hypothetical data for both population and sample, and

iv. Identify and justify the most suitable sampling method for the scenario.

COVID-19 Annual Booster Vaccination Public Sentiment:

Alternative Sampling Methods:

● Simple Random Sampling: The probability of selection for every person in the population is the same.

● Stratified Sampling: It portion’s the population in different groups it refers to as samples to the specific characteristics like age or health and then samples a size from each section.

Significance:

● Simple Random Sampling: Helps in achieving equal representation of the population’s attitude in the poll (Ali, et. al., 2024, p2(2)).

Sampling Process:

● Population: All people residing in Victoria, P.E.I., Canada.

● Simple Random Sampling: A list of one thousand individuals should be obtained by using a random number generator.

● Stratified Sampling: Here, the population is split into groups, specific categories, or zones, in this case, age groups, and you then take a random sample of 200 people from each group.

Most Suitable Method:

Therefore, the most suitable sampling technique would be the Stratified Sampling to ensure representation of different subgroups’ attitudes in the demographically diverse society.

Socioeconomic Status in Rural Victoria:

Alternative Sampling Methods:

● Cluster Sampling: The entire clusters of the population are selected by random, for instance if the population is classified into villages.

● Systematic Sampling: Using a list of the population every individual is chosen in the sequence of every n.

Significance:

● Cluster Sampling: Saves on the extenders that may be used in handling items physically when conducted among geographically dispersed people and/or groups.

● Systematic Sampling: Easy to apply and it guarantees that samples are taken in a systematic manner in different places in the population.

Sampling Process:

● Population: To conclude, the following are the target customers; Residents in rural areas of Victoria.

● Cluster Sampling: Sample any 10 villages and then give an interview to all the people from these villages.

● Systematic Sampling: Enumerate all the rural inhabitants, and then include every fiftieth person in the sample will suffice the intended goal.

Most Suitable Method:

Cluster Sampling is most suitable because in ,field research , especially where the respondents are spread out in the larger rural areas, one is assured of adequate coverage within the selected clusters.

Question 2 (10 marks)

A. A quality control team conducted a study to measure the time it takes to complete a specific quality check in a manufacturing plant. They collected data from a random sample of 18 quality checks and found that the average time was 9.7 minutes, with a standard deviation of 1.5 minutes.

Required:

Assuming that the times are normally distributed, calculate the 99% confidence interval for the mean time required to complete the quality check.

To calculate the 99% confidence interval for the mean time required to complete the quality check, we use the formula for the confidence interval for a population mean when the population standard deviation (????) is known:

B. Your younger brother is confused about some fundamental statistics concepts and struggles to understand whether these concepts are similar or different, as well as their application in business decision-making. As someone who has studied statistics, you promised to help him. Assume his doubts are primarily about data classification, scales of measurement, and the use of sample statistics as point estimators for population parameters.

Required:

Provide a brief explanation based on the content learned in this unit supported by examples.

Data classification pertains to the grouping of data according to some or several characteristics in statistics. This assists in analysis since we can study entities and their features, compare them and make conclusions. For instance, grouping the customer according to their age (18-25, 26-35, etc. ) assists the companies to market to specific niches. Scales of measurement sort data in according to the characteristics of the values with them and identify what statistic tests can be used. The four main scales are:

● Nominal Scale: Categorization of objects that do not have a prior arranged order for example; categories of cars: sedan and SUV.

● Ordinal Scale: Order categories that have equal differences in between, but without equal steps (e. g., positions in a race: first, second, third).

● Interval Scale: These are numerical scales in which variations in the values have meaning as indicated by the origin but there is no actual zero point such as temperature in Celsius or Fahrenheit.

● Ratio Scale: Continuous variables grouped into ordinal classes that are bound by a true zero point and meaningful ratio relationships exist ( e. g. , height and weight).

Sample statistics are the outcomes obtained from sample data which is used to estimate the population parameters. For example sample mean (x̄) represents the population mean (μ) and sample standard deviation (s) represents population standard deviation (σ). Sample statistics involve applying particular statistical values on the population that a business is conducting a study on, for example, average customer satisfaction score from a sample survey. Familiarity with these ideas enables one to analyze information competently and to make efficient business decisions.