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OMIS3200: QUANTITATIVE METHODS
CASE WORKSHOP 2
Exploring Sampling, Confidence Intervals, and Hypothesis Testing
Instructions
This workshop is divided into two parts, designed to improve your understanding of
sampling, confidence intervals, and hypothesis testing through practical application. Part I
focuses on the analysis of stock returns, using confidence intervals and hypothesis testing
techniques. Part II considers the DoorDash Delivery case study.
Working in pairs and discussing your findings can be helpful. If you encounter any
difficulties with the exercises, do not hesitate to seek assistance from me.
Part I: Stock Return Analysis
In this section, you will analyze the daily returns (percentage change in the daily price of a
stock) of four companies: Tesla, Apple, Google, and Microsoft. You will find the data in a file
named StockReturns.xlsx.
a) Produce descriptive statistics and plot a histogram for each of the 4 companies.
b) Construct 95% confidence intervals for the mean of each company.
c) For each company, can you reject the null hypothesis that the mean return is zero (use a
5% significance level)?
d) For each company, can you reject the claim that returns are 1. 5 % on average (use a 5%
significance level)?
e) Is it reasonable to say that there is no significant difference between the mean of Tesla and
Apple returns (use a 5% significance level)? Answer the same question for Apple and
Microsoft.
t-Test: Two-Sample Assuming Unequal Variances
Tesla Apple
Mean 0.00106044 0.
Variance 0.000986118 0.
Observations 251 251
Hypothesized Mean Difference 0
df 329
t Stat -0.
P(T<=t) one-tail 0.
t Critical one-tail 1.
P(T<=t) two-tail 0.
t Critical two-tail 1.
Solutions to the Exercise on Confidence Intervals and Hypothesis Tests
In this section, we demonstrate how to solve parts (b) through (e) mostly using data from one
company, Tesla, as an example. This should guide you in applying a similar approach to other
companies’ data:
(b) From the Descriptive Statistics output, we find Tesla’s estimated mean return (sample
mean) to be 0. 0011. The formula for the confidence interval when the population standard
deviation (𝜎) is unknown and estimated by the sample standard deviation (𝑠) is:
[𝑥̅ ± 𝑡𝛼
2
,𝑛− 1
]
Here, 𝑠 = 0. 0314 and 𝑛 = 251. The 𝑡 critical value 𝑡
𝛼
2
,𝑛− 1
can be obtained in Excel using:
𝛼
2
,𝑛− 1
- 025 , 251 − 1
So, the confidence interval becomes:
[ 0. 0011 ± 1. 967
] =
[
]
[
]
A quicker method in Excel involves directly adding and subtracting the “Confidence Level”
to and from the mean:
[ 0. 0011 ± 0. 003903 ] = [− 0. 00284 , 0. 00496 ] = [− 0. 284 %, 0. 496 %]
(c) Since the confidence interval [− 0. 284 %, 0. 496 %] includes zero, we cannot reject the
hypothesis that Tesla’s mean return is zero at the 95% confidence level.
(d) The interval [− 0. 284 % , 0. 496 %] does not include 1. 5 %, allowing us to reject the
hypothesis that Tesla's mean return is 1.5% with 95% confidence.
(e) The 95% confidence interval for Apple's mean returns is [− 0. 04 %, 0. 27 %], which
overlaps with Tesla’s
[
]
. At first glance, this suggests no significant difference
between the two. However, a formal hypothesis test is necessary for a definitive conclusion.
Using Excel’s “two-sample mean test with unequal variances” , as shown above, we see that
the t-stat value of − 0. 050797 is less than the t-critical (two-tail) value of 1. 967 , indicating
that we should not reject the null hypothesis (𝐻 0
) of no significant difference between the
average Apple and Tesla daily stock returns.
a) Estimate the proportion of deliveries completed within 3 5, 4 0, or 4 5 minutes for
orders within an 8 - mile radius.
b) Let us call the proportion of on-time deliveries 𝑝. There is a known formula for the
95% confidence interval of this quantity:
[𝑝̂ − 1. 96 ⋅
]
where 𝑝̂ is the proportion of the sample and 𝑛 is the sample size. Using this
formula, compute a 95% confidence interval for the proportion of on-time
deliveries for each of these time frames.
c) Assuming DoorDash completes 1000 deliveries within an 8-mile limit, calculate a
95% confidence interval for the total dollar amount of penalties it would incur for
late deliveries at each of the delay thresholds of 35, 40, or 45 minutes from part
(a). Consider that DoorDash issues a $ 15 credit to customers for each delay.
3. Speed Comparison Between Dashers: In striving to enhance its competitive edge
and operational efficiency:
a) Perform a statistical test to determine if there are significant differences in
average delivery speeds for each pair of Dashers 1, 4, 7, and 9 pairwise.
Grading Rubric
The assignment (only Part II) will be graded according to the following rubric, with each category
contributing to the overall score.
Category Weight
Evaluating Dasher Performance: The report must accurately address parts (a)
and (b). Partial credit will be granted for solutions that are not entirely correct,
based on the extent of their correctness. [Each part 20%.]
Delivery Time Commitment and Customer Satisfaction: The report must
accurately address parts (a) and (b). Partial credit will be granted for solutions
that are not entirely correct, based on the extent of their correctness. [Each part
20%.]
Applicability at Workplace : The report must accurately address part (a).
Partial credit will be granted for solutions that are not entirely correct, based on
the extent of their correctness.
