BM3034 : Concepts on the Continuous Probability Distribution - Management Assignment Help

Assignment Task:

Task:

Learning Outcomes  After the completion of this assignment, learners will be able to: 
Solve problems using concepts on the continuous probability distribution. Select a representative sample when conducting a business survey research by applying theories of the sampling distribution of the sample means. Perform inferential statistics on real-life data using statistical estimation and hypothesis testing techniques. 
3. Reauirements  3.1 Continuous Probability Distribution (25 marks) 
(i) 
Each learner most use one (1) of the following three (3) continuous probability distribution cases listed below based on the instructions given. For learners whose admission number ends with the numbers "0,1,2,3" solve Case 3.1 (i)(a). For learners whose admission number ends with the numbers "4,5,6" solve Case 3.1 (i)(b). For learners whose admission number ends with the numbers .7,13,9" solve Case 3.1 (I)(c). 
(a) According to a director of a hospital, the body temperature of an adult is normally distributed with a mean of 36.9°C and a standard deviation of 0.5°C. 
(b) Based on the research by a marketing manager of a weight loss programme, the weight of female individuals aged 3040 is normally distributed with a mean 55 kg and a standard deviation of 14 kg. 
(c) According to a sport & wellness professional, the BMI of a male teenager aged 20-30 is normally distributed with a mean of 22.2 kg/m2 and a standard deviation of 1.7 kg/m2 
(ii) Based on your case assigned from above, solve the following problems using continuous probability distribution techniques. Diagram is not needed for this section. 
(a) State the mean, standard deviation and variance. (3 marks) 
Individual Assignment Guide/ BM3034 / Page 3 
(b) Describe how the normal curve will look when the mean increases and the standard deviation cienreases. (4 marks) 
(c) Calculate the amount for the top and bottom kth percentage of the population, where k is your register number in your class register. Shoot all the steps required. (12 marks) 
(d) Calculate the probability that an individual in the population (X) is more than 5 standard deviations bigger than the population mean. Explain if it is possible to find such an individual in the population with reference to your case scenario. (6 marks) 
(iii) Write down your answers with appropriate workings in your report. State clearly the case that you are solving. Example: Continuous Probability Distribution Case 3.1 (i)(a) or Case 3.1 (i)(b) or Case 3.1 (i)(c)  
3.2 Sampling Distribution of the Sample Means (25 marks) 
(i) A survey research is a tool used by businesses to obtain feedback from their customers, suppliers or employees. One of the requirements to obtain good feedback from their respondents when conducting a survey is to select a representative sample for the survey. 
For this assignment, you are the business personnel who is conducting a survey for your company to obtain an estimate on the population mean. Write a reflection on how the concepts and theorem(s) taught in the topic "Sampling Distribution of the Sample Means" can facilitate your decision-making process in conducting the business sunmy research, such as choosing an appropriate sample size for the survey as well as other considerations, costs and benefits. 
(ii) Your reflection should provide discussion and explanation for the following areas: 

(d) Calculate the probability that an individual in the population (X) is more than 5 standard deviations bigger than the population mean. Explain if it is possible to find such an individual in the population with reference to your case scenario. (6 marks) 
(iii) Write down your answers with appropriate workings in your report. State clearly the case that you are solving. Example: Continuous Probability Distribution Case 3.1 (i)(a) or Case 3.1 (i)(b) or Case 3.1 (i)(c)  
3.2 Sampling Distribution of the Sample Means (25 marks) 
(i) A survey research is a tool used by businesses to obtain feedback from their custorners, suppliers or ernployees. One of the requirements to obtain good feedback from their respondents when conducting a survey is to select a representative sample for the survey. 
For this assignment, you are the business personnel who is conducting a survey for your company to obtain an estimate on the population mean. Write a reflection on how the concepts and theorem(s) taught in the topic "Sampling Distribution of the Sample Means" can facilitate your decision-making process in conducting the business survey research, such as choosing an appropriate sample size for the survey as well as other considerations, oosts and benefits. 
(ii) Your reflection should provide discussion and explanation for the following areas: 
(a) How do the concepts and theorem(s) in the topic "Sampling Distribution of the Sample Means" influence your decision in choosing an appropriate (or minimum) sample size for the survey? (10 marks) 
(b) Is a bigger sample better for the survey? Discuss the benefits of having a bigger sample for the survey with reference to the standard error. Any possible costs associated with a bigger sample selected? How do you decide on the sample size for your survey? (6 marks) 
(c) Besides the knowledge gained in the topic, suggest any three (3) measures that you can undertake to obtain good feedback from your respondents when conducting the survey. Be as innovative as possible and provide reasons and elaborations to support your suggestions. (9 marks) 
Individual Assignment Guide / BM3034 / Page 4 
3.3 Statistical Estimation (25 marks) 
(i) Each leamer must use one (1) of the following two (2) statistical estimation cases listed below based on the instructions given. For leamers whose admission number ends with letters "A" to "0", solve Case 3.3 (i)(a). For learners whose admission number ends with letters ..1." to "Z", solve Case 3.3 (i)(b). The sample size taken for each learner is n=15+k, where k is your register number in your class register. For example, if your class register number is 1, the sample size that you will select is n=15+1=16. Thus, you will select the first n=16 from the relevant sample data in Appendix 1 and perform the appropriate calculations. On the other hand, if your class register number is 20, the sample size that you will select is n=15+20=35. Thus, you will select the first n=35 from the relevant sample data in Appendix 1 and perform the appropriate calculations. 
(a) Covid19 has highlighted the importance of strict hygiene and more frequent cleaning and disinfection of commercial accommodation. A hotel is keen to automate the disinfection process and is evaluating a new cleaning and disinfection robot fora month. Currently it takes the housekeeping staff an average 01 45 minutes to disinfect a room. The hotel management aims to reduce the average disinfection time by half. If the upper confidence limit of the interval estimate on the population mean disinfection time by the robot does not meet the target, 11_' t. A random sample 
 

Statistical Estimation (25 marks) 
(i) Each leamer most use one (1) of the following two (2) statistical estimation cases listed below based on the instructions given. For leamers whose admission number ends with letters "A" to "0", solve Case 3.3 (i)(a). For leamers whose admission number ends with letters ..1." to "Z", solve Case 3.3 (i)(b). The sample size taken for each learner is n=15+k, where k is your register number in your class register. For example, if your class register number is 1, the sample size that you will select is n=15+1=16. Thus, you will select the first n=16 from the relevant sample data in Appendix 1 and perform the appropriate calculations. On the other hand, if your class register number is 20, the sample size that you will select is n=15+20.35. Thus, you will select the first n=35 from the relevant sample data in Appendix 1 and perform the appropriate calculations. 
(a) Covid19 has highlighted the importance of strict hygiene and more frequent cleaning and disinfection of commercial accommodation. A hotel is keen to automate the disinfection process and is evaluating a new cleaning and disinfection robot for a month. Currently it takes the housekeeping staff an average of 45 minutes to disinfect a room. The hotel management aims to reduce the average disinfection time by half. If the upper confidence limit of the interval estimate on the population mean disinfection time by the robot does not meet the target, the robot will not be purchased, vice versa. A random sample of hotel rooms cleaned by the robot was selected and the disinfection time was recorded during the trial month. The data collected is shown in a table in Appendix 1. 
(b) E-commerce and online shopping have become extremely popular. A small online business prides itself in its ability to fill customer orders in less than six working days, on average. Recently, the operations manager feels that the order fulfilment might have slackened due to an increase in the business volume. To check if this is the case, the operations manager selected a random sample of recent customer orders to determine the number of days required to fill the orders. If the upper confidence limit of the interval estimate on the population mean order fulfilment time does not meet the target, the manager will conduct a comprehensive operations review. The data collected is shown in a table in Appendix 1. 
(ii) Based on your case assigned from above, solve the following problems using statistical estimation techniques. Diagram is not needed in this section. 
(a) Copy the sample data tabulated in appendix 1 and paste them into MS Excel and perform descriptive statistics on the data using MS 
Individual Assignment Guide / BM3034 / Page 5 
(p) 
(c) 
Excel Data Analysis Tool Pak. Refer to the detailed illustration and instnictions on how to perform descriptive statistic, from the video lectures taught in class and in BlackBoard. Save the raw data and the output of the descriptive statistics on the same worksheet and submit them in the appendix section. (2 marks) 
State the point estimates for the population mean and standard deviation. (2 marks) 
Calculate the 95% confidence interval for the population mean. Show all the steps required. (9 marks) 
(d) Determine the conclusion for your case above. (3 marks) 
(e) Suggest how to improve the reliability and precision of the confidence interval calculated. u late theoyn minimum e size to reduce the width of (9 marks) 
 

(d) Determine the conclusion for your case above. (3 marks) 
(e) Suggest how to improve the reliability and precision of the confidence interval calculated. Calculate the minimum sample size to reduce the width of confidence interval calculated by half. (9 marks) (iii) Write down your answers with appropriate workings in your report. State clearly the case that you are solving. Example: Statistical Estimation Case 3.3 (i)(a) or Case 3.3 (i)(b)  
3.4 Hypothesis testing (25 marks) 
(I) 
Each learner must solve one (1) of the following two (2) hypothesis testing cases listed below based on the instructions given. For learners whose admission number ends with an odd number (1,3,5,7.9), solve Case 3.4 (i)(a). For learners whose admission number ends with an even number (2,4,6,8,0), solve Case 3.4 (i)(b). The sample size taken for each learner is n=44-k, where k is your register number in your class register. For example, if your class register number is 1. the sample size that you will select is n=44-1=43. Thus, you will select the first n=43 from the relevant sample data in Appendix 1 and perform the appropriate calculations. On the other hand, if your class register number is 20, the sarnple size that you will select is n=44-20=24. Thus, you will select the first n=24 from the relevant sample data in Appendix 1 and perform the appropriate calculations. 
(a) The marketing department of a company had just completed an outbound marketing campaign. The average sales target set by management was $6,500 per customer. The marketing manager convened a study to determine if the campaign target had been met. If the average sales was below the target, corrective actions would be undertaken. The data collected from a random sample of sales generated from the campaign is shown in a table in Appendix 1. Determine if corrective actions needed to be undertaken with a hypothesis test at 1% level of significance. 
Individual Assignment Guide / BM3034 / Page 6 
(b) A company is contemplating to purchase a new Customer Relationship Management (CRM) system after the trial period to improve customer service. The customer service director of the company wants to deterrnine if the average customer satisfaction level has improved with the new systern. Previously, the average custorner satisfaction level has been 75 points. If the average custorner satisfaction level has improved, the company would purchase the new system. To measure the satisfaction level of its customers during the trial period, a survey was commissioned. The data collected from a random sample of customers tracked under the new system is shown (eatable in Appendix. Determine if the company should purchase the new system with a hypothesis test at 5% significance level. 
(ii) Using the relevant sample data tabulated for the above cases in appendix 1, solve the assigned case using hypothesis testing methodology. Diagram is not needed in this section. 
(a) 
Copy the relevant sample data tabulated in appendix 1 and paste them into MS Excel and perform descriptive statistics on the data using MS Excel Data Analysis Tool Pak. Refer to the detailed illustration and instructions on how to perform descriptive statistics from the video lectures taught in class and in BlackBoard. Save the raw data and the output of the descriptive statistics on the same worksheet and submit them in the appendix section. (2 marks) 
(b) State the values of the sample mean and sample standard deviation. (2 marks) 
(c) Determine the conclusion for your case above using a hypothesis test. Show all the steps required. (11 marks) 
(c11 Describe tvoe I and II errors. (4 marks) 
 

satisfaction level has improved, the company would purchase the new system. To measure the satisfaction level of its customers during the trial period, a survey was commissioned. The data collected from a random sample of customers tracked under the new system is shown in a table in Appendix. Determine if the company should purchase the new system with a hypothesis test at 5% significance level. 
(ii) Using the relevant sample data tabulated for the above cases in appendix 1, solve the assigned case using hypothesis testing methodology. Diagram is not needed in this section. 
(a) 
Copy the relevant sample data tabulated in appendix 1 and paste them into MS Excel and perform descriptive statistics on the data using MS Excel Data Analysis Tool Pak. Refer to the detailed illustration and instructions on how to perform descriptive statistics from the video lectures taught in class and in BlackBoard. Save the raw data and the output of the descriptive statistics on the same worksheet and submit them in the appendix section. (2 marks) 
(b) State the values of the sample mean and sample standard deviation. (2 marks) (c) Determine the conclusion for your case above using a hypothesis test. Show all the steps required. (11 marks) (d) Isg_j_0.2 type I and II errors. (4 marks) (e) Explain the consequences of committing type I and type II errors respectively. Suggest how to adjust the significance level to minimise type I and type II errors respectively. (6 marks) 
(iii) Write down your answers with appropriate workings in your report. State clearly the case that you are solving. Example: Hypothesis testing Case 3.4 filfal or Case 3.4 111(b) 
4. Submissions 
;Report Format • A written report of not more than 6 pages (excluding cover page and appendices) • Arial Font size 12 with single spacing must be submitted by each individual leamer. • Please assign your file name for submission with the following format: 
Individual Assignment Guide / BM3034 / Page 7 
BM3034_Class_AdminNumber_Name e.g. BM3034_BA_123456A_John Tan Ah Seng Your report for submission should include the following parts: 
i) Cover Page Include a cover page with the assignment title (BM3034 ICA 3: Business Statistics individual Assignment), name and admission number of the learner. 
Continuous Probability Distribution  Solutions for the case assigned to you. Sampling Distribution of the Sample Means 
iii) A reflection of not more than 250 words (inclusive within the 6-page limit) on the topic that consists of discussion and explanation for the areas required as mentioned above. Statistical Estimation  iv) Solutions for the case assigned to you. 
Hypothesis Testing v) Solutions for the case assigned to you. 
vi) Appendix, providing the raw sample data of the statistical estimation and hypothesis testing cases assigned and the output of the descriptive statistics generated by the MS Excel Data Analysis Tool Pak. 
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