ECOM1000 – Analytics for Decision Making

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Faculty of Business and Law | School of Economics, Finance and Property CRICOS Provider Code 00301J
ECOM1000 – Analytics for Decision Making
Module 8 – Confidence Interval
Learning Outcomes
After completing this Tutorial/Lab you should be able to:
1. Construct and interpret confidence interval estimate for the mean
2. Construct and interpret confidence interval estimate for the proportion
3. Determine the sample size necessary to develop a confidence interval for the mean or proportion
4. Recognise how to use confidence interval estimates in Auditing (Limited)
Part 1 –Short answer questions
Question 1
Suppose a 95% confidence interval for μ turns out to be (1000, 2100).
Give a definition of what it means to be “95% confident” in an inference.
A. 95% of the observations in the entire population fall in the given interval.
B. In repeated sampling, the population parameter would fall in the given interval 95% of the time.
C. 95% of the observations in the sample fall in the given interval.
D. In repeated sampling, 95% of the intervals constructed would contain the population mean.
To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the
following will result in a reduced interval width?
A. Increase the population.
B. Increase the sample size.
C. Increase the confidence level.
D. Increase the sample mean.
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Faculty of Business and Law | School of Economics, Finance and Property CRICOS Provider Code 00301J
ECOM1000 – Analytics for Decision Making
Question 2
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a
suburb of Sydney. The investor’s main concern is the total market value of the 3,605 houses in the suburb. From past
experience, the standard deviation of market housing prices is estimated to be $81,000. The investor commissioned a
statistical consulting group to take a sample of 200 houses and obtained a sample average market price of $450,000 and
a sample standard deviation of $77,400. The consulting group also found out that the average differences between market
prices and appraised prices was $250,000 with a standard deviation of $6,800. Also, the proportion of houses in the sample
that are appraised for higher than the market prices is 0.24. (Refer to Key formulas section on page 308 of textbook)
A. What will be the 90% confidence interval for the average market price of the houses in the suburb constructed by
the consulting group?
B. What will be the 90% confidence interval for the population proportion of houses that will be appraised for higher
than the market prices?
C. If the investor wants a 95% confidence on estimating the true population average market price of the houses in the
suburb to be within $20,000, how large a sample will he need?
Question 3
Statistical sampling is widely used for the purposes of estimation in auditing due to its many advantages. Which of the
following is NOT an advantage of statistical sampling in auditing?
A. It allows auditors to generalise their results to the population with a known sampling error.
B. It allows auditors to combine, and then evaluate collectively, samples collected by different individuals.
C. The results are objective and defensible.
D. None of the above.
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Faculty of Business and Law | School of Economics, Finance and Property CRICOS Provider Code 00301J
ECOM1000 – Analytics for Decision Making
Part 2 – Data exercise
A busy landscaping supplies company sells wood chips for garden mulch. The mulch is sold by the cubic metric and delivered
to households in a small truck. Each truckload is expected to be 4 cubic metres. The company decides to conduct an audit
of actual load volumes by smoothing and measuring samples of loads for a two-week period. The data file mulch.xlsx
contains the volume (in cubic metres) from a sample of 368 truckloads of cypress pine mulch and from a sample of 330
truckloads of cedar wood chips.
a. Produce a line plot for each type of mulch.
b. Produce a box plot for each type of mulch.
c. Produce a histogram for each type of mulch.
d. Using the histogram data produce a cumulative percentage polygon/chart.
e. Calculate the descriptive statistics (Data analysis toolpak) for each type of mulch. Select the confidence level for
mean option (use 95%).
f. Manually calculate the 95% confidence level for the mean of each type of mulch i.e. sample mean ± critical
value*standard error. Note that the confidence level (95%) from (e) is equal to critical value*standard error.
g. Based on the results from (a) to (f), what conclusions can you reach about the two types of mulch.
Part 3 – Pearson MyLab
Please logon to MyLab and complete the following tasks:
1. Please ensure that you have finished the Mylab activities from module 6 and module 7. The recorded tutorials/labs
from module 6 and module 7 provide a brief overview of the homework questions.
2. Complete the homework questions based on module 8 topics.
It is important that students complete Mylab tasks on a weekly basis since the final assessment in this unit will be
completed using MyLab.