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MTHS3003 Coursework description
创建日期：2024-05-16 14:47:58
所属分类：数学mathematics
标签： MTHS3003
Coursework description

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MTHS3003 Coursework description

Make sure that you are using the data corresponding to your student number and that you
have read the coursework submission requirements provided in the guidance document.
The owner of a coffee shop on campus has commissioned you to analyse some data and prepare a report to
help them in their planning for the next academic year.
The coffee shop is open 8am-6pm Monday to Friday and 10am-4pm at the weekends (Saturday and Sunday).
The coffee shop owner has provided the following data in csv.files:
• The number of customers served in each 5 minute interval throughout the day on a Tuesday.
(Coffee_Tuesday_20468731.csv)
• The number of customers served in each 5 minute interval 8:30-9:00am; Monday to Friday for a 10
week period. (Coffee_early_20468731.csv)
• The number of customers served on each Saturday and Sunday for a 10 week period. (Cof-
fee_weekend_20468731.csv)
• The total income per day for a 10 week period along with a number of covariates which could be helpful
in explaining income. (Coffee_income_20468731.csv)
The coffee shop owner has asked you to:
1. Provide an exploratory analysis of the number of customers served in 5 minute intervals using the data
provided in Coffee_Tuesday_20468731.csv [10 marks]
Note: The coffee shop owner states the busy times are usually 8-10am and 12pm-2pm with the quiet time
after 4pm.
2. The coffee owner proposes that customer demand in a 5 minute interval follows a X ∼ Po(λ) distribution.
Estimate the customer demand during the weekday early morning (8:30-9am) busy period using
Coffee_early_20468731.csv. Due to staff and space constraints, the maximum number of customers
that can be served in a 5 minute interval is 12. [20 marks]
a. Find the maximum likelihood estimate of λ.
Suppose that an extra member of staff would enable the coffee shop to serve an additional 2
customers per 5 minute interval if there is the demand
b. Estimate how often the extra member of staff will be busy.
c. Given that an extra member of staff would cost £20 per hour and the average profit per customer
is £2.10, is it worth the owner having an extra member of staff between 8:30-9:00am?
3. The coffee shop owner suspects that the early morning busy period varies by day of the week. [13
marks]
a. Does the data in Coffee_early_20468731.csv support the coffee owners suspicions? (Answer the
question by the means of an appropriate hypothesis test and/or exploratory analysis.)
b. How does the answer to question 3.(a) affect the conclusions drawn in question 2? (You should
not perform any further analysis in relation to question 2.)
4. The coffee shop owner is interested in weekend customer numbers. Use the data in Cof-
fee_weekend_20468731.csv to address the following questions and discuss your conclusions. [20
1
marks]
a. Are the data consistent with the coffee shop owners assumption that the mean number of
customers on Saturdays and Sundays are 250 and 230, respectively?
b. Are the data consistent with the coffee shop owners assumption that the mean difference in the
number of customers between Saturday and Sunday is at least 20?
5. The coffee shop owner wants to know how income per day (response variable) depends on the following
covariates: [22 marks]
• Day of the week
• Mean number of staff working throughout the day
• Number of meal options
• Daily temperature (oC)
• Term time (yes/no)
a. Find the best model for predicting income using the data in Coffee_income_20468731.csv.
b. Comment on the model fit and effect of the selected covariates on income.
c. Estimate the level of income on a day with the following covariate information:
A Saturday not in term time with daily temperature 19.7oC, on average 3.9 members of staff
working and 1 meal options.

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