ACTIVITY BRIEF FOR ASSESSMENT 2
ACADEMIC YEAR 2021 – 2022 – SPRING
Course  BCO127 – Management Statistics (2CH/3ECTS) 
Instructor  Louisa Carlse 
AssignmentTutorOnline
Participation in all assessment activities stated in this document is required. An overall course total of 70
points is required to pass the course. Due dates and times are always in Geneva time.
Assessment 2  
Description  Due date and time 
Weight of course total 
Task 2.1: Quiz on Sampling Distributions Assessment type: Quiz Description: Multiple choice questions on the topic of Sampling Distributions. For further details of this assessment task, please consult the activity description on the relevant week of the course site. 
28 Mar. 22 14:00 
5% 
Task 2.2: Quiz on Tests of Significance Assessment type: Quiz Description: Multiple choice questions on the topic of Tests of Significance. For further details of this assessment task, please consult the activity description on the relevant week of the course site. 
01 May. 22 14:00 
5% 
Main task Task 2.3: Final Assignment Assessment type: Written assignment Description: Assignment on Sampling Distributions, Confidence Intervals, Tests of Significance and Regression. Questions are mostly practical – students will submit a spreadsheet file. See sections below for further details. 
09 May. 22 14:00 
30% 
INSTRUCTIONS
Main task
• Graphs should be titled, and all axes should be adequately labeled
• The submitted spreadsheet must include all formulas used and all necessary calculations to prove
steps taken for final answers
FORMAT
Your submission must meet the following formatting requirements:
• Submit one file only.
• Required file format for main submission: Excel spreadsheet (.xlsx).
• Additional file format for additional deliverables: Not applicable.
• Additional file requirements: None.
Other details:
• No specific formatting specifications
• No specific number of words required
• No referencing required
LEARNING OUTCOMES
• Understand concepts, formulas and techniques of statistics through exercises and applied examples;
• Understand statistical language, statistical context, uncertainty, and develop statistical thinking;
• Design statistical models, perform analysis, and solve realworld problems;
• Interpret results of statistical analysis
ASSESSMENT CRITERIA
Criteria  Accomplished (A) 
Proficient (B)  Partially proficient (C) 
Borderline (D)  Fail (F) 
Computation  Result and process are correct, and answer is well explained (process is detailed). Minor details may cause deduction of points. 
Minor errors leading to wrong result, but computation is clear and process is generally correct. 
Some important errors revealing some confusion, but partially correct process. Seemingly correct process and correct result, but no adequate explanation is provided 
Important errors revealing significant misunderstanding of relevant concepts, but the process is not entirely wrong. 
Wrong result, lacking any coherent explanation. 
Written Answers & Interpretations 
Well detailed and justified answered, statistically correct. 
Well detailed and justified answered, with some statistical incorrections. 
Revels understanding of some concepts, but there is some confusion regarding relevant topics. 
Incorrect answer from the statistical point of view, but explanation is not completely incoherent or wrong 
Wrong answer and incoherent or absent justification. 
Graph  Correct, readable and well presented, properly titled and labeled (including axes, and units if needed) 
Some minor readability or presentation. 
Important errors, but graphs still conveys most relevant information. 
Serious errors rendering the graph almost useless, but correct type of graph and variables are used. 
No graphs is presented, or graph completely misses the point (incorrect graph type and/or variables) 
ADDITIONAL INFORMATION
Question 1 (15 Marks)
Answer the following questions:
a) What is the difference between statistic and parameter? (5 points) 
b) The variable Y follows a continuous uniform distribution. What is the type of distribution followed by the sampling distribution of the mean of Y, for a sample size of 80? Justify. (5 points) 
c) What is the meaning of “sampling distribution of the mean“ of a certain variable X, for a given sample size n? (5 points) 
Question 2 (25 Marks)
A certain successful restaurant operates with a waiting line, without reservations. The managers want to know how much time in minutes (variable X) are the customers waiting and decide to run a simple study. Before this study, the distribution of X was completely unknown. During a specific day, a total of 80 customers were asked to measure the waiting time. Initially, a sample of 40 measurements (lunch) was obtained: 

23.9  21.5  27.0  0.0  30.9  9.3  22.2  29.3 
5.8  0.0  20.9  17.5  25.1  29.1  27.1  6.2 
15.8  21.9  25.0  13.9  21.7  16.7  13.9  19.6 
23.0  8.0  11.1  18.0  28.6  18.6  9.1  34.3 
1.1  21.0  10.3  23.2  7.1  5.2  36.4  18.4 
a) Based on this sample, compute a confidence interval for the mean of X, for a confidence level of 95%. (10 points) 

b) A new batch of 40 measurements arrives in the evening (dinner), allowing for a sample size increase (n = 80). Compute a new interval estimate for the mean, for the same confidence level of 95%, taking both the lunch and the dinner measurements into account (n = 80). (5 points) 

32.9  35.5  33.7  43.4  39.0  29.0  38.0  32.7 
35.3  22.0  38.4  31.5  25.5  39.4  41.7  22.1 
36.3  42.3  33.7  29.4  0.0  36.5  32.5  29.2 
30.6  34.7  11.2  34.5  8.7  23.2  36.7  19.2 
33.4  44.0  39.2  33.7  15.7  26.5  0.0  46.5 
c) Compare your answers to 2.1 and 2.2 and justify the difference(s). In your opinion, should the managers attempt to obtain separate interval estimates for lunch and dinner? Justify. (5 points) 

d) Assuming the standard deviation of the population is equal to the sample standard deviation (sample of 80 measurements), determine the sample size required for a confidence interval with a margin of error of 3 minutes and a confidence level of 95%. (5 points) 
Question 3 (30 Marks)
A company that produces wireless headphones is testing a new battery for their products. In order to evaluate the capacity of the new batteries, a sample of 50 headphones from a specific model are equipped with the new battery and tested for autonomy. The current average battery autonomy is 5.2 hours. Test results from the sample of headphones equipped with the new battery produce a sample mean of 5.6 hours and a sample standard deviation of 0.8 hours. For a significance level of 5%, can we conclude that the autonomy of the new batteries is different from the autonomy of the batteries currently in use? 
a) Should this test for the mean be twotailed, righttailed or lefttailed? Justify your answer. (5 points) 
b) State the null hypothesis (5 points) 
c) State the alternative hypothesis. (5 points) 
d) Compute the pvalue and comment on the result. (5 points) 
e) Compute the rejection region (test statistic) and use it to determine whether the null hypothesis should be rejected, for a significance level of 5%. Do not forget to write a conclusion that refers to the realworld problem, i.e. a conclusion that people without a background in Statistics may understand. (5 points) 
f) Could you have answered the previous question (determining the test result for a significance level of 5%) without computing the rejection region? Justify your answer. (5 points) 
Question 4 (30 Marks)
A company that manufactures solar energy systems performs a study on the relationship between average power obtained from a specific solar panel (X1, in kilowatt [kW]) and average daily rainfall (X2, in mm). A sample of 30 solar panels is placed in different geographical locations and, after a few weeks, the average power obtained by each solar panel is registered. Parallel measures of average daily rainfall for those exact same locations are obtained: 
X1. Average power [kW] 
X2. Average daily rainfall [mm] 
1.65  0.69 
1.19  17.47 
0.85  24.43 
0.89  27.13 
1.15  25.77 
1.43  7.53 
1.74  6.74 
1.52  1.54 
1.51  14.50 
1.39  6.34 
1.84  2.58 
1.33  17.07 
0.65  31.97 
1.13  13.68 
1.58  11.92 
1.62  7.50 
0.92  31.33 
1.81  1.37 
1.80  6.32 
1.65  2.58 
1.69  1.89 
1.06  27.57 
1.56  0.87 
1.41  11.74 
1.92  1.56 
1.36  5.88 
1.29  14.73 
1.27  13.58 
1.50  3.33 
1.60  3.50 
a) Compute the correlation between the two variables. (5 points)  
b) In your opinion, which of the two variables (X1 and X2) should be considered as the independent or explanatory variable in this case? Justify your answer. (5 points) 

c) Based on your answer to the previous question, determine the coefficients of the linear regression model. Write down the complete linear regression model. (5 points) 

d) Compute the coefficient of determination (r² or R squared) of this model. What would the value of the coefficient of determination be if the variables in the regression model were inverted – (independent or explanatory variable (X) becomes Y, and dependent or response variable (Y) becomes X)? Justify. (5 points) 

e) Predict the value of X2 for a solar panel that produces an average of 0.8 kW, using the linear model you’ve determined in (c). Predict the value of X1 for a panel installed in a location with an average daily rainfall of 20 mm, using the linear model you’ve determine in (c). (5 points) 

f) Obtain an appropriate graphical representation of the linear regression model. (note: in addition to the original graph, please include or paste the graph as a picture to avoid any formatting or conversion issue). (5 points). 
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