BCLO001 Business Statistics Assignment: Analysis of Exercise Duration Among Singaporean Students

Introduction

Objective of the Assignment

To effectively organise, summarise, analyse and present statistical data (with meaningful conclusions) based on real issues through application of the appropriate concepts of statistics.

Case Study Background

The National Population Health Survey 2023 showed that 78.5 per cent of Singapore residents aged 18 to 74 had sufficient total physical activity, up from 74.9 per cent in 2022.

Singapore Physical Activity Guidelines encourage residents to do a range of activities with a recommended target of at least 150 minutes of moderate to vigorous physical activity (exercise) per week.

After reading the above article, Justin, a student from Temasek Polytechnic, was interested in estimating the amount of time (duration) Singaporeans engage in exercise weekly. He surveyed a random sample of 100 students from Temasek Polytechnic recently.

Besides the exercise duration, he also surveyed the types of exercise engaged in by those surveyed. The types of exercises included jogging, swimming, ball games, and others.

The data of the 100 students surveyed is in the worksheet “Data”.

He has requested you to help him with some data collection and statistical analysis.

• a. Collect an additional 20 data points to make the sample size 120.
• b. Apply the statistical concepts and tools that you have learnt and answer the following questions.

Submission Requirement

This is an individual assignment. Your work should be typed in this EXCEL file for each question. Please write your Name and Student ID on the Cover Page for submission. The report is to be named as BCLO001_StudentName.xlsx.

You are also to include the additional raw data you collected and append it to the “Data” worksheet provided (Row 102 onwards). For the Excel outputs for each of the questions, pls append them in the question worksheet itself.

Important to Note

• One question on one worksheet, as indicated in the EXCEL file provided to you.
• All presentation and working steps are to be clearly shown in the questions worksheet. Otherwise, you will be given zero marks for that part of the question.
• You are to use EXCEL to attempt this assignment.
• You are encouraged to use the functions that were taught to you to construct your frequency table and conduct the statistical analysis.

Disclaimer

This exercise is developed for the purpose of data analysis and interpretation.

Question 1 (35 marks)

a) Using the sample data collected by you and Justin, apply the relevant Excel functions/reports to compute the three measures of central tendency and the three measures of dispersion on the weekly exercise duration. Describe the sampled data using the statistical measures.

b) Construct the frequency distribution for the exercise duration using a class interval of 50 minutes with 0 as the lower limit of the first class.

c) Support part b) with a histogram to show the distribution of the data. Describe the shape of the histogram.

d) Do you have a reason to believe that males spend more time exercising than females? Provide a summary report to answer the above question. Support your reasoning with relevant statistical measures and/or charts.

Question 2 (25 marks)

Construct a contingency table using the sampled data collected by gender and type of exercise.

Using the contingency table, answer the following questions:

a) What is the probability that a person chosen plays ball games?

b) What is the probability that a person chosen is a female and jogs?

c) What is the probability that a person chosen, engage in other activities?

d) Given that a person who swims, what is the probability that this person is a male?

e) Given that a female is chosen, what is the probability that she swims?

Question 3 (30 marks)

a) The Singapore Physical Activity Guidelines encourage residents to have at least 150 minutes of exercise weekly. Construct a 95% Confidence Interval for the exercise duration by Singaporeans per week. Interpret and discuss whether Justin can conclude that the mean exercise duration of Singaporeans is at least 150 min per week. List assumptions that you have made.

b) Justin believes that Singaporeans are too busy with their work and unable to spend more than 150 mins to exercise per week. At the 5% level of significance, can you agree with the claim made by Justin? List any assumptions that you have made.

Question 4 (10 marks)

Summarise your findings from this project that you have done with Justin on the exercise duration of Singaporeans. Comment on TWO (2) concerns that you have on the analysis.