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ECOM1000 – Analytics for Decision Making
Module 7 – Sampling Distributions
Learning Outcomes
After completing this Lab/Tutorial you should be able to:
1. Interpret the concept of the sampling distribution
2. Calculate probabilities related to the sample mean
3. Recognise the importance of the Central Limit Theorem (CLT)
4. Calculate probabilities related to the sample proportion
PART 1 – Short answer questions
Question 1
A statistic calculated from a sample is used to estimate the corresponding
A. sample.
B. parameter.
C. distribution.
D. statistic.
Question 2
The Central Limit Theorem is important in statistics because
A. for any sized sample, it says the sampling distribution of the sample mean is approximately normal.
B. for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the
sample size.
C. for a large n, it says the population is approximately normal.
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Faculty of Business and Law | School of Economics, Finance and Properties CRICOS Provider Code 00301J
ECOM1000 – Analytics for Decision Making
D. for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape
of the population.
Question 3
Australian football salaries averaged $150,000 with a standard deviation of $80,000 in a recent year. Suppose a sample
of 100 football players was taken.
a) What was the standard error for the sample mean salary?
b) Find the approximate probability that the average salary of the 100 players is less than $140,000.
Question 4
The Central Limit Theorem allows one to make inferences about the population mean but requires that one knows the
specific shape of the population distribution.
A. True
B. False
Question 5
According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random
samples of size 50 are selected.
a) What is the average of all the sample proportions of customers who will make a purchase after visiting the web site?
b) What is the standard deviation of all the sample proportions of customers who will make a purchase after visiting
the web site?
c) What proportion of the samples will have between 20% and 30% of customers who will make a purchase after
visiting the web site?
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Faculty of Business and Law | School of Economics, Finance and Properties CRICOS Provider Code 00301J
ECOM1000 – Analytics for Decision Making
PART 2 – Data Exercise
Download the data file “Restaurant_times.xlsx” from the data section in module 7.
(a) Briefly describe the contents of this data file
(b) Calculate the descriptive statistics for each of the variables in the data. Provide a brief commentary on the results.
(c) Produce a scatterplot of the waiting and serving time. Is there a relationship between these two variables?
(d) Is there a difference in the mean waiting time between restaurants that serve complimentary drink versus the ones
that do not?
(e) Extract a sample of 30 waiting times and calculate the mean waiting time for the sample. How does this value
compare to the mean waiting time for all 100 restaurants (part (b))?
(f) Repeat step (e) 4 to 8 times i.e. extract more samples of size 30 and calculate the mean waiting time for each
sample. How do these values compare to the mean waiting time for all 100 restaurants (part (b))?
(g) Calculate the overall mean waiting time across all samples i.e. the average of all the average values from each
sample. How does this value compare to the mean waiting time for all 100 restaurants?
PART 3 – Pearson Mylab
Please logon to MyLab and complete the following tasks.
1. Complete the homework questions based on module 7 topics.
2. Please ensure that you have finished the Mylab activities from module 1, 2, 3 and 5. These included the Candidate
agreement, Orientation questions and Homework questions (Module 1,2,3 and 5). The recorded tutorials/labs from
modules 1, 2, 3 and 5 provide a brief overview of the homework questions in Mylab. This will help you prepare for the
quiz (week 8).
Please note that the quiz (week 8) will be done using MyLab and will contain content from module 1 through to module 5
(inclusive). If you are having issues with obtaining access to Mylab, please re-read the instructions (available in the welcome
module). If you are still unsuccessful, please send an email to ecom1000@curtin.edu.au explaining the issue.