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School for Business and Society


Module Code: MAN00035C

Module Title: Quantitative Analysis in Management

Module Leader: Şule Şahin

Open/Closed Assessment: Open

Maximum Word Count: 1200 words

Release Date: End of Week 4

Submission Deadline: 9th of May 2025

Weighting: 50%


Important information

A penalty of five marks will be deducted for late submissions that are made within the
first hour after the deadline. Submissions that are more than one hour late but within the
first 24 hours of the deadline will incur a penalty of ten marks. After the first 24 hours
have passed, ten marks will be deducted for every 24 hours (or part thereof) that the
submission is late for a total of 5 days. After 5 days it is treated as a non-submission and
given a mark of zero. The consequences of non-submission are serious and can include
de-registration from the University.

If you are unable to complete your open assessment by the submission date indicated
above because of Exceptional Circumstances you can apply for an extension. If
unforeseeable and exceptional circumstances do occur, you must seek support and
provide evidence as soon as possible at the time of the occurrence. Applications must be
made before the deadline to be considered.

Full details of the Exceptional Circumstances Policy and claim form can be found here:
https://www.york.ac.uk/students/studying/progress/exceptional-circumstances

If you submit your open assessment on time but feel that your performance has been
affected by Exceptional Circumstances you may submit an Exceptional Circumstances
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Affecting Assessment claim form by 7 days from the published assessment submission
deadline. If you do not submit by the deadline indicated without good reason your claim
will not be considered.

Please take proper precautions to safeguard your work and remember to make
backup copies of your data. The University provides all its students with storage
space on the University server and you should save and back up any work in
progress on this server on a regular basis. Computer failure and theft of your
equipment or storage media are not considered exceptional circumstances and
extensions cannot be granted for work lost for these reasons.

The University has guidance on the use of AI in assessments available here. This
details appropriate and inappropriate use of digital tools. Inappropriate use will be
considered academic misconduct, and penalised accordingly

Word count requirements

The word count for this assignment is 1200 words.

You must state on the front of your assignment the number of words used and this will be
checked.

The main text for this assignment must be word-processed in Arial, font 12, double
spacing, minimum 2cm margins all around.

You must observe the word count specified in this assignment brief. The School has a
policy of accepting variations to the recommended word count of plus or minus 5%.

What does this mean for you?

Markers will mark your work up to the word count maximum plus 5% and then will stop
marking; therefore all words which are in excess of the word count plus 5% will not be
marked.

Where your word count is more than 5% below that specified, it is likely that this will result
in a lack of analytical depth or relevant content, which will be reflected in the mark
assigned.


What is in the word count?

The word count includes:

- the main text, including in-text reference citations and quotations.

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The word count does not include:

- Appendices. These may be used to include supporting data, which may be too
detailed or complex to include as a Table. They are not a device to incorporate
material, which would otherwise cause you to exceed the word limit.

- Title page
- Contents page
- Abstract/executive summary
- Tables, figures, legends
- Reference lists
- Acknowledgements

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Assignment:

Question 1:
You are tasked with comparing the average processing times of two different
manufacturing machines, Machine A and Machine B, over 10 days. Your goal is to
determine if there is a significant difference in their average daily processing times. Below
are the processing times (in hours) for both machines:


Day Machine A
(hours)
Machine B
(hours)
Day 1 7.5 8.2
Day 2 7.8 8.5
Day 3 7.4 8.0
Day 4 7.6 8.6
Day 5 7.7 7.8
Day 6 7.9 8.9
Day 7 7.5 8.4
Day 8 7.6 8.0
Day 9 7.8 9.0
Day 10 7.7 8.3


Required:

a) Calculate the mean and variance of processing times for each machine.
[5 marks]

b) Perform an appropriate statistical test to investigate if there is a significant
difference in the average daily processing times between Machine A and Machine
B, using a 5% significance level. In your analysis, you should state the null and
alternative hypothesis, the critical value at the 5% significance level and discuss if
the null hypothesis may be rejected using appropriate test statistics. Support your
conclusion by producing a graph of the distribution.

NOTE: In this question, you should assume that the processing times for
both machines are independent samples, are both normally distributed and
that the true (but unknown) variances are the same.
[15 marks]

TOTAL: 20 marks


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Question 2:

A company is conducting a study to determine if there is a relationship between the
preferred type of vacation (Beach, Adventure, and Cultural) and the age group of
consumers (20-29 years, 30-39 years, and 40-49 years). A survey was conducted, and
the results based on a random sample of 300 consumers are presented in the table
below:

Preferred Vacation Type
Age Group Beach Adventure Cultural
20-29 50 30 20
30-39 40 50 30
40-49 30 40 10

Required:

a) Calculate the expected number of consumers that would prefer each type of
vacation for each age group, assuming that vacation preference is independent of
the age group.
[5 marks]

b) Determine if there is a significant association between the preferred type of
vacation and the age group at the 2.5% significance level. In your analysis, you
should state the null and alternative hypothesis, the critical value at the 2.5%
significance level and discuss if the null hypothesis may be rejected using
appropriate test statistics. Support your conclusion by producing a graph of the
distribution.
[15 marks]

c) Prepare a report on the results (500-600 words). Do this assuming a wide
audience with differing levels of knowledge in the area of statistics and hypothesis
testing (therefore, explain the processes involved in simple but formal language).
In particular, discuss all of the following:

- The idea behind hypothesis testing and why this is important;
- The process performed in order to obtain the results, the key assumptions in this
process, and the appropriateness of these assumptions to the question;
- The result and how to interpret this.

Within your report, feel free to bring in other knowledge you have from the question
that you feel would best describe the process and result to a wide audience. This is
meant to be a brief report which you would happily present in a business format.

[20 marks]
TOTAL: 40 marks
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Question 3:

ABC Corporation claims that the average delivery time for their products is faster than
the competitor's average of 10 days. To test this claim, a random sample of 40 deliveries
was taken, and the average delivery time was found to be 9.4 days, with a standard
deviation of 1.5 days.

Required:

Examine if ABC Corporation's claim is supported by the data at the 5% significance level.
In your analysis, you should state the null and alternative hypothesis, the critical value at
the 5% significance level and discuss if the null hypothesis may be rejected using
appropriate test statistics. Support your conclusion by producing a graph of the
distribution. Comment on your choice of distribution considering the sample size.

TOTAL: 15 marks


























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Question 4:

A fitness centre is investigating the relationship between the average monthly
subscription revenue (in £) (SR) and the number of new members (denoted by NM)
joining per month. Below is the SPSS output summarising the regression analysis:

Model Summary

Model R R Square Adjusted R
Square
Std. Error of the
Estimate
1 0.812 0.659 0.649 350.47


ANOVA

Model Sum of
Squares
df Mean Square F Sig.
Regression 1,860,400 1 1,860,400 15.14 <0.001
Residual 962,500 15 64,166.67
Total 2,822,900 16


Coefficients

Model Unstandardized
Coefficients (B)
Std. Error Standardized
Coefficients
(Beta)
t Sig.
(Constant) 5000 850 5.882 <0.001
Number of
New Members
(NM)
75 19.35 0.812 3.891 <0.001


Required:

a) State, giving a brief explanation, which variable you think should be the dependent
variable.
[2marks]

b) What is the equation for the line of best fit? Comment on the size and significance
of the estimated coefficients. [2 marks]

c) Plot the line of best fit and calculate the predicted average subscription revenue
for months with 20 and 50 new members; add these data points to your plot. Briefly
explain how the method of obtaining the line of best fit works.

[8 marks]

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d) Comment on the correlation between the variables and the overall measure of
goodness of fit for the model. [3 marks]

e) Comment on the nature and reliability of the estimated relationship. What
additional information might enhance your confidence in the conclusions drawn?

[10 marks]

TOTAL: 25 marks





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PERCENTAGE POINTS OF THE T-DISTRIBUTION
One Tail 5% 2.5% 1% 0.5% 0.1% 0.05%
Two Tails 10% 5% 2% 1% 0.2% 0.1%
1 6.314 12.706 31.821 63.657 318.309 636.619
2 2.920 4.303 6.965 9.925 22.327 31.599
3 2.353 3.182 4.541 5.841 10.215 12.924
4 2.132 2.776 3.747 4.604 7.173 8.610
5 2.015 2.571 3.365 4.032 5.893 6.869
6 1.943 2.447 3.143 3.707 5.208

5.959
7 1.895 2.365 2.998 3.499 4.785 5.408
8 1.860 2.306 2.896 3.355 4.501 5.041
9 1.833 2.262 2.821 3.250 4.297 4.781
10 1.812 2.228 2.764 3.169 4.144 4.587
11 1.796 2.201 2.718 3.106 4.025

4.437
12 1.782 2.179 2.681 3.055 3.930 4.318
13 1.771 2.160 2.650 3.012 3.852 4.221
14 1.761 2.145 2.624 2.977 3.787 4.140
15 1.753 2.131 2.602 2.947 3.733 4.073
16 1.746 2.120 2.583 2.921 3.686

4.015
17 1.740 2.110 2.567 2.898 3.646 3.965
18 1.734 2.101 2.552 2.878 3.610 3.922
19 1.729 2.093 2.539 2.861 3.579 3.883
20 1.725 2.086 2.528 2.845 3.552 3.850
25 1.708 2.060 2.485 2.787 3.450

3.725
30 1.697 2.042 2.457 2.750 3.385 3.646
40 1.684 2.021 2.423 2.704 3.307 3.551
50 1.676 2.009 2.403 2.678 3.261 3.496
60 1.671 2.000 2.390 2.660 3.232 3.460
∞ 1.645 1.960 2.326 2.576 3.090 3.291

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Standard Normal Distribution Tables: Values represent AREA to the LEFT of z.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-3.90 0.00005 0.00005 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00003 0.00003
-3.80 0.00007 0.00007 0.00007 0.00006 0.00006 0.00006 0.00006 0.00005 0.00005 0.00005
-3.70 0.00011 0.00010 0.00010 0.00010 0.00009 0.00009 0.00008 0.00008 0.00008 0.00008
-3.60 0.00016 0.00015 0.00015 0.00014 0.00014 0.00013 0.00013 0.00012 0.00012 0.00011
-3.50 0.00023 0.00022 0.00022 0.00021 0.00020 0.00019 0.00019 0.00018 0.00017 0.00017
-3.40 0.00034 0.00032 0.00031 0.00030 0.00029 0.00028 0.00027 0.00026 0.00025 0.00024
-3.30 0.00048 0.00047 0.00045 0.00043 0.00042 0.00040 0.00039 0.00038 0.00036 0.00035
-3.20 0.00069 0.00066 0.00064 0.00062 0.00060 0.00058 0.00056 0.00054 0.00052 0.00050
-3.10 0.00097 0.00094 0.00090 0.00087 0.00084 0.00082 0.00079 0.00076 0.00074 0.00071
-3.00 0.00135 0.00131 0.00126 0.00122 0.00118 0.00114 0.00111 0.00107 0.00104 0.00100
-2.90 0.00187 0.00181 0.00175 0.00169 0.00164 0.00159 0.00154 0.00149 0.00144 0.00139
-2.80 0.00256 0.00248 0.00240 0.00233 0.00226 0.00219 0.00212 0.00205 0.00199 0.00193
-2.70 0.00347 0.00336 0.00326 0.00317 0.00307 0.00298 0.00289 0.00280 0.00272 0.00264
-2.60 0.00466 0.00453 0.00440 0.00427 0.00415 0.00402 0.00391 0.00379 0.00368 0.00357
-2.50 0.00621 0.00604 0.00587 0.00570 0.00554 0.00539 0.00523 0.00508 0.00494 0.00480
-2.40 0.00820 0.00798 0.00776 0.00755 0.00734 0.00714 0.00695 0.00676 0.00657 0.00639
-2.30 0.01072 0.01044 0.01017 0.00990 0.00964 0.00939 0.00914 0.00889 0.00866 0.00842
-2.20 0.01390 0.01355 0.01321 0.01287 0.01255 0.01222 0.01191 0.01160 0.01130 0.01101
-2.10 0.01786 0.01743 0.01700 0.01659 0.01618 0.01578 0.01539 0.01500 0.01463 0.01426
-2.00 0.02275 0.02222 0.02169 0.02118 0.02068 0.02018 0.01970 0.01923 0.01876 0.01831
-1.90 0.02872 0.02807 0.02743 0.02680 0.02619 0.02559 0.02500 0.02442 0.02385 0.02330
-1.80 0.03593 0.03515 0.03438 0.03362 0.03288 0.03216 0.03144 0.03074 0.03005 0.02938
-1.70 0.04457 0.04363 0.04272 0.04182 0.04093 0.04006 0.03920 0.03836 0.03754 0.03673
-1.60 0.05480 0.05370 0.05262 0.05155 0.05050 0.04947 0.04846 0.04746 0.04648 0.04551
-1.50 0.06681 0.06552 0.06426 0.06301 0.06178 0.06057 0.05938 0.05821 0.05705 0.05592
-1.40 0.08076 0.07927 0.07780 0.07636 0.07493 0.07353 0.07215 0.07078 0.06944 0.06811
-1.30 0.09680 0.09510 0.09342 0.09176 0.09012 0.08851 0.08691 0.08534 0.08379 0.08226
-1.20 0.11507 0.11314 0.11123 0.10935 0.10749 0.10565 0.10383 0.10204 0.10027 0.09853
-1.10 0.13567 0.13350 0.13136 0.12924 0.12714 0.12507 0.12302 0.12100 0.11900 0.11702
-1.00 0.15866 0.15625 0.15386 0.15151 0.14917 0.14686 0.14457 0.14231 0.14007 0.13786
-0.90 0.18406 0.18141 0.17879 0.17619 0.17361 0.17106 0.16853 0.16602 0.16354 0.16109
-0.80 0.21186 0.20897 0.20611 0.20327 0.20045 0.19766 0.19489 0.19215 0.18943 0.18673
-0.70 0.24196 0.23885 0.23576 0.23270 0.22965 0.22663 0.22363 0.22065 0.21770 0.21476
-0.60 0.27425 0.27093 0.26763 0.26435 0.26109 0.25785 0.25463 0.25143 0.24825 0.24510
-0.50 0.30854 0.30503 0.30153 0.29806 0.29460 0.29116 0.28774 0.28434 0.28096 0.27760
-0.40 0.34458 0.34090 0.33724 0.33360 0.32997 0.32636 0.32276 0.31918 0.31561 0.31207
-0.30 0.38209 0.37828 0.37448 0.37070 0.36693 0.36317 0.35942 0.35569 0.35197 0.34827
-0.20 0.42074 0.41683 0.41294 0.40905 0.40517 0.40129 0.39743 0.39358 0.38974 0.38591
-0.10 0.46017 0.45620 0.45224 0.44828 0.44433 0.44038 0.43644 0.43251 0.42858 0.42465
0.00 0.50000 0.49601 0.49202 0.48803 0.48405 0.48006 0.47608 0.47210 0.46812 0.46414
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Standard Normal Distribution Tables: Values represent AREA to the LEFT of z.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.00 0.50000 0.50399 0.50798 0.51197 0.51595 0.51994 0.52392 0.52790 0.53188 0.53586
0.10 0.53983 0.54380 0.54776 0.55172 0.55567 0.55962 0.56356 0.56749 0.57142 0.57535
0.20 0.57926 0.58317 0.58706 0.59095 0.59483 0.59871 0.60257 0.60642 0.61026 0.61409
0.30 0.61791 0.62172 0.62552 0.62930 0.63307 0.63683 0.64058 0.64431 0.64803 0.65173
0.40 0.65542 0.65910 0.66276 0.66640 0.67003 0.67364 0.67724 0.68082 0.68439 0.68793
0.50 0.69146 0.69497 0.69847 0.70194 0.70540 0.70884 0.71226 0.71566 0.71904 0.72240
0.60 0.72575 0.72907 0.73237 0.73565 0.73891 0.74215 0.74537 0.74857 0.75175 0.75490
0.70 0.75804 0.76115 0.76424 0.76730 0.77035 0.77337 0.77637 0.77935 0.78230 0.78524
0.80 0.78814 0.79103 0.79389 0.79673 0.79955 0.80234 0.80511 0.80785 0.81057 0.81327
0.90 0.81594 0.81859 0.82121 0.82381 0.82639 0.82894 0.83147 0.83398 0.83646 0.83891
1.00 0.84134 0.84375 0.84614 0.84849 0.85083 0.85314 0.85543 0.85769 0.85993 0.86214
1.10 0.86433 0.86650 0.86864 0.87076 0.87286 0.87493 0.87698 0.87900 0.88100 0.88298
1.20 0.88493 0.88686 0.88877 0.89065 0.89251 0.89435 0.89617 0.89796 0.89973 0.90147
1.30 0.90320 0.90490 0.90658 0.90824 0.90988 0.91149 0.91309 0.91466 0.91621 0.91774
1.40 0.91924 0.92073 0.92220 0.92364 0.92507 0.92647 0.92785 0.92922 0.93056 0.93189
1.50 0.93319 0.93448 0.93574 0.93699 0.93822 0.93943 0.94062 0.94179 0.94295 0.94408
1.60 0.94520 0.94630 0.94738 0.94845 0.94950 0.95053 0.95154 0.95254 0.95352 0.95449
1.70 0.95543 0.95637 0.95728 0.95818 0.95907 0.95994 0.96080 0.96164 0.96246 0.96327
1.80 0.96407 0.96485 0.96562 0.96638 0.96712 0.96784 0.96856 0.96926 0.96995 0.97062
1.90 0.97128 0.97193 0.97257 0.97320 0.97381 0.97441 0.97500 0.97558 0.97615 0.97670
2.00 0.97725 0.97778 0.97831 0.97882 0.97932 0.97982 0.98030 0.98077 0.98124 0.98169
2.10 0.98214 0.98257 0.98300 0.98341 0.98382 0.98422 0.98461 0.98500 0.98537 0.98574
2.20 0.98610 0.98645 0.98679 0.98713 0.98745 0.98778 0.98809 0.98840 0.98870 0.98899
2.30 0.98928 0.98956 0.98983 0.99010 0.99036 0.99061 0.99086 0.99111 0.99134 0.99158
2.40 0.99180 0.99202 0.99224 0.99245 0.99266 0.99286 0.99305 0.99324 0.99343 0.99361
2.50 0.99379 0.99396 0.99413 0.99430 0.99446 0.99461 0.99477 0.99492 0.99506 0.99520
2.60 0.99534 0.99547 0.99560 0.99573 0.99585 0.99598 0.99609 0.99621 0.99632 0.99643
2.70 0.99653 0.99664 0.99674 0.99683 0.99693 0.99702 0.99711 0.99720 0.99728 0.99736
2.80 0.99744 0.99752 0.99760 0.99767 0.99774 0.99781 0.99788 0.99795 0.99801 0.99807
2.90 0.99813 0.99819 0.99825 0.99831 0.99836 0.99841 0.99846 0.99851 0.99856 0.99861
3.00 0.99865 0.99869 0.99874 0.99878 0.99882 0.99886 0.99889 0.99893 0.99896 0.99900
3.10 0.99903 0.99906 0.99910 0.99913 0.99916 0.99918 0.99921 0.99924 0.99926 0.99929
3.20 0.99931 0.99934 0.99936 0.99938 0.99940 0.99942 0.99944 0.99946 0.99948 0.99950
3.30 0.99952 0.99953 0.99955 0.99957 0.99958 0.99960 0.99961 0.99962 0.99964 0.99965
3.40 0.99966 0.99968 0.99969 0.99970 0.99971 0.99972 0.99973 0.99974 0.99975 0.99976
3.50 0.99977 0.99978 0.99978 0.99979 0.99980 0.99981 0.99981 0.99982 0.99983 0.99983
3.60 0.99984 0.99985 0.99985 0.99986 0.99986 0.99987 0.99987 0.99988 0.99988 0.99989
3.70 0.99989 0.99990 0.99990 0.99990 0.99991 0.99991 0.99992 0.99992 0.99992 0.99992
3.80 0.99993 0.99993 0.99993 0.99994 0.99994 0.99994 0.99994 0.99995 0.99995 0.99995
3.90 0.99995 0.99995 0.99996 0.99996 0.99996 0.99996 0.99996 0.99996 0.99997 0.99997



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