Business Management Question 2022

National Institute of Business Management
Advanced Certificate in Data Analytics 21.2
Submission Date: - On or before 5.00 pm on 05th April 2022
You can either use Excel, SPSS, or R if needed
Take-Home Exam
Question 01 (10 marks)
Customers arrive at a checkout counter in a department store according to a Poisson distribution
at an average of seven per hour. During a given hour, what are the probabilities that
a. no more than three customers arrive?
b. at least two customers arrive?
c. exactly five customers arrive?
d. Find the mean and variance of the number of customers during a given hour.
e. What is the probability that exactly two customers arrive in the two-hour period of time
between 2:00 P.M. and 4:00 P.M. (one continuous two-hour period)?
Question 02 (10marks)
The Toyota Camry is one of the best-selling cars in North America. The cost of a previously
owned Camry depends on many factors, including the model year, mileage, and
condition. To investigate the relationship between the car’s mileage and the sales price for
Camrys, the following data show the mileage and sale price for 19 sales (PriceHub Web
site, February 24, 2012).

Miles (1000s)
Price
($1,000s)
22 16.2
29 16
36 13.8
47 11.5
63 12.5
77 12.9
73 11.2
87 13
92 11.8
101 10.8
110 8.3
28 12.5
59 11.1
68 15
68 12.2
91 13
42 15.6
65 12.7
110 8.3
a. Develop a scatter chart for these data with miles as the independent variable. What
does the scatter chart indicate about the relationship between price and miles?
b. Develop an estimated regression equation showing how price is related to miles. What
is the estimated regression model?
c. Suppose that you are considering purchasing a previously owned Camry that has been
driven 60,000 miles. Use the estimated regression equation developed in part b to
predict the price for this car. Is this the price you would offer the seller?

Question 03 (10 marks)
A marketing analyst collected the following data which recorded the ages (in years) of random
samples of 25 purchasers and 20 non-purchasers of a certain brand of toothpaste
Purchasers: 28 22 44 33 55 63 45 31 60 54 53 58 52 52 66 28 27 62 36 22
54 60 45 38 41
Non-purchasers: 34 35 23 44 52 46 28 48 28 34 33 52 41 32 34 30 31 29 30
28
From this sample
(a) Check whether the average age of purchaser is 45
(b) Does it appear that age is significant in distinguishing between the two groups?
Question 04 (10 marks)
Suppose we want to compare the mean daily sales (£) at two restaurants located in the same city
and have the following data collected over a two-week period:
From this sample does it appear that there is a significant difference in the average daily takings
between the two restaurants?

Question 05 (10 marks)
The following monthly turnovers (£000s) and profits (£000s) for a chain of 15 shops was
recorded.
(a) Construct the scatter plot.
(b) It is of interest to quantify how the two variables are related and to be able to predict
profit for various turnovers (use correlation coefficient to answer this).
Question 06 (10 marks)
The personnel manager of a manufacturing company is interested in forecasting whether a
particular applicant will become a good telesales person. Data has been collected on the 30 most
recent appointments that records as a dependent variable their first month’s sales (units of a
certain product sold) together with the following 5 potential explanatory variables:
 age (years);
 sex (dummy coded as 0=female, 1=male);
 ucas points tariff;
 anxiety test score on a scale out of 10 where anxiety increases with number;
 aptitude test score on a scale out of 100 where aptitude increases with number.

Sales Age Gender UCAS anxiety aptitude
56 28 Male 14 0.6 47
37 24 Male 260 3.3 21
52 27 Female 30 1.5 49
55 24 Male 40 3 75
60 28 Male 50 3.2 65
37 27 Male 60 4.9 11
40 25 Female 70 0.7 4
42 24 Female 80 2.7 15
57 27 Female 80 2.7 66
43 27 Female 90 1.4 9
48 28 Female 90 3.8 21
55 28 Male 90 2.2 58
58 31 Male 100 2.1 44
59 26 Female 100 2.7 83
49 24 Female 110 3 21
64 27 Male 110 0.3 92
50 30 Female 120 4.4 9
48 22 Female 120 0.1 23
56 30 Female 140 0.6 8
41 30 Male 140 2.3 27
57 28 Female 140 4.6 50
59 25 Female 150 3.9 98
52 28 Female 160 0.9 58
50 29 Female 170 6 28
60 31 Male 180 1.8 36
58 28 Female 180 4.5 65
83 30 Male 16 4.8 94
64 26 Male 220 4.5 73
73 28 Female 240 3.1 98
54 33 Male 260 1.8 30

Obtain the relationship between the variables using scatter plots and correlations.
Question 07 (10 marks)
The following time series plot displays the quarterly smart phone sales for four years.
(a) Briefly explain the properties of the above series.
(b) From the following three models, select a suitable model for the above series. Be sure to
provide reasons for your selection.
𝑀𝑜𝑑𝑒𝑙 1: 𝑌̂𝑡 = 6.07 − 1.36𝑄1𝑡 − 2.03𝑄2𝑡 − 0.304𝑄3𝑡
𝑀𝑜𝑑𝑒𝑙 2: 𝑌̂𝑡 = 6.07 + 0.14𝑡
𝑀𝑜𝑑𝑒𝑙 3: 𝑌̂𝑡 = 6.07 − 1.36𝑄1𝑡 − 2.03𝑄2𝑡 − 0.304𝑄3𝑡 + 0.14𝑡
(c) Using the selected model, forecast the sales for the next year (year 5).
Question 08 (10 marks)
The American Community Survey(ACS), is a large survey undertaken by the US Census Bureau
in the years between decennial censuses. For this analysis project, you are given a subset of the
Public Use Micro Data sample for Oregon from 2013 that corresponds to households that contain
opposite-gender married couples (you may assume this is a simple random sample of such
households in Oregon).

Description of Variables in acs.xlsx data file;
Column name Variable
household A unique ID number for each household
age_husband Age in years of husband
age_wife Age in years of husband
income_husband Total annual income of husband, can include wages, retirement, interest,
social security, self-employment income.
income_wife Total annual income of wife, as above
bedrooms Number of bedrooms in the home
electricity Monthly cost of electricity
gas Monthly cost of gas
number_children The number of children in the home
internet Does the home have internet access?
mode The way the household took the survey
own Do the residents own with or without a mortgage or rent?
language The primary language spoken in the home
decade_built The decade the home was built
The relevant data are given in the acs.xlsx file. You are allowed to use any statistical software
to perform your analysis.
1. Obtain the numerical summaries for the income of the husband, income of the wife, mode
(The way the household took the survey), and the cost of the electricity. Interpret your
results. You should provide relevant graphs of the data involved too (Histogram, box plot,
etc…).
2. Summarize the frequency of the ownership of the house according to the number of
bedrooms. What observations can you make about the ownership of the house based on the
number of bedrooms? Draw a side-by-side bar plot to illustrate this.
3. The surveyor claims that the average cost of the electricity of this selected household is at
least 130. Assume that the cost of the electricity is normally distributed and use a 0.05 level
of significance to test the surveyor’s claim.

4. Explore the relationship between the Age of husband and the age of wife. Compute the
sample correlation coefficient and show the relationship graphically.
Build a simple linear regression model and interpret your results.
5. In households with no children, do husbands tend to be older than their wives? By how
much?
6. Do households in houses built in the 1960s or earlier spend more on electricity, than those
built in the 1970s or later? By how much?
(Hint: You could answer for 5th and 6th questions using this data and the tools we have learnt
so far. You may subset as appropriate to answer your question.)
7. Can the surveyor conclude that the average income of husband is greater than average
income of wife?
Conduct a hypothesis test at the 5% level of significance.
What are the assumptions you need to perform this test?
(Hint: Check whether the variances are equal before conducting the hypothesis test)
Question 09 (10 marks)
The average height of females in a certain college freshman class has historically been 162.5
centimeters with a standard deviation of 6.9 centimeters. Is there reason to believe that there has
been a change in the average height if a random sample of 50 females in the present freshman
class has an average height of 165.2 centimeters? Use a P-value in your conclusion. Assume the
standard deviation remains the same.

Question 10 (10 marks)
(a). Briefly define the following terms.
(i). Parameter
(ii). Statistic
(iii). Estimator
(iv). Estimate
(v). Point estimate
(vi). Interval estimate
(b). A random sample of 25 cereal boxes showed 𝑋̅= 372.5. The company has specified  =
15 grams. Does an average box of cereal contain more than 368 grams of cereal? (Test at
the 5% level of significance)
(c). Past data indicate that the time taken to download the Facebook home page is normally
distributed with mean 8 seconds and a standard deviation of 2 seconds. A random sample
of 16 occasions is taken and the mean time (that is X ) is calculated.
(i). Calculate the mean value and standard deviation of the average time taken to
download the Facebook home page.
(ii). Calculate the probability that the average time taken to download the Facebook
home page is less than 9 seconds.
(iii). Calculate the probability that the average time taken to download the Facebook
home page is between 7.0 and 9.5 seconds.