Describe about the Applied Business Decision Models?
XYZ Apparel, a division of TBJD Clothing, is alarge national chain of women’s apparel stores.Data was collected for 100 in-store credit card transactions from all its stores during one day while a special promotion was run.
An Excel file containing the data is posted on the Blackboard EMBA 633 002 course website on the “Announcements” page under the Exam1 announcement.
For the quantitative variables, calculate the mean, median, mode, and midrange of all the sampled data.
|
Statistic |
# Items |
Net Sales ($) |
Age (years) |
|
Mean |
3.22 |
77.60 |
43.08 |
|
Median |
2.00 |
59.71 |
42.00 |
|
Mode |
1.00 |
31.60 |
46.00 |
|
Midrange |
9.00 |
150.41 |
49.00 |
For the quantitative variables, calculate the first quartile (Q1), third quartile (Q3), midquartile, interquartile range (IQR) of all the sampled data.
|
Statistic |
# Items |
Net Sales ($) |
Age (years) |
|
Q1 |
1.00 |
39.60 |
32.00 |
|
Q3 |
4.00 |
100.90 |
50.00 |
|
Midquartile |
2.50 |
70.25 |
41.00 |
|
IQR |
3.00 |
61.30 |
18.00 |
For the quantitative variables, calculate the sample range (R), standard deviation (s), and coefficient of variation (CV) of all the sampled dat
|
Statistic |
# Items |
Net Sales |
Age |
|
R |
16.00 |
274.36 |
58.00 |
|
s2 |
7.49 |
3098.59 |
153.49 |
|
s |
2.74 |
55.66 |
12.39 |
|
CV |
84.97 |
71.73 |
28.76 |
For each of problems 1 through 15 below, enter your short responses below each statement. Report anycalculated results rounded to three (3) decimal places.
What is the population that is being sampled?
Customers buying XYZ apparel.
a. Is the data for each quantitative variable discrete or continuous?
Items is discrete while net sales and age is continuous
What is the measurement scale of each quantitative variable?
Ratio
Of the sampled data:
How old is a customer expected to be?
Customer is expected to be between the age of 49 years
How many items is a customer expected to purchase perin-store credit card transaction?
Customer is expected to buy 9 # items.
How much money is a customer expected to spend per in-store credit card transaction?
Customer is expected to spend $ 150.41.
In general:
How old is a customer expected to be?
Mean age is 43.08 years
How many items is a customer expected to purchase perin-storecredit card transaction?
Mean # items is 3.22
How much money is a customer expected to spend per in-store credit card transaction?
Mean net sales is $ 77.60
How good is the calculated sample mean at representing (a) number of items purchased, (b) net sales amount, and (c) customer age?Briefly state why.
To represent net sales amount and customer age mean can be used to represent the population as they are continuous variables while # items is a discrete variable with few extreme values which are influencing mean.
How strongly should the mean(a) number of items purchased, (b) net sales amount, and (c) customer age be expected? Briefly state why for each.
Mean should be used to represent age as midrange is close to mean while for # items and net sales there is lot of difference between mid range and mean. Also, it can be noticed that there are few high values for # items and net sales which influence mean to a greater extent.
What is the most usual (a) number of items purchased, (b) net sales amount, and (c) customer age?
Most usual – a) # items is 1, b) net sales amount is 31.60, c) customer age is 46.00
Suppose a customer spends $65. Is this a high or low amount? Briefly state why.
We will test it through z-test –
x=$65, µ = 77.60, σ = 55.66, n =100
z = (x-µ)/σ/√n = (65-77.60)/55.66/10 = -2.264
From z-table,
p(z) = p(-2.264) = .0119
The p-value obtained is less than 5% level of significance, hence, the amount spend is low.
Do the sample data for (a) number of items purchased, (b) net sales amount, and (c) customer age show high or low relative variability? Briefly state why for each.
Age shows low variability with a value of 28.76% while # items and net sales shows high variability with values of 84.97 % and 71.73 %, respectively. For # items and net sales there are few high values which influence mean and causes variation.
Are the data for (a) number of items purchased, (b) net sales amount, and (c) customer age skewed or not skewed? If skewed, which way?Briefly state why for each.
All the three variables # items, age and net sales are skewed to the right with most of the values bunched up towards right with mean greater than median.
Describe the clustering of the inner half of the ordered data for (a) number of items purchased, (b) net sales amount, and (c) customer age. Briefly state why for each.
Clustering = IQR/R
1) # items – 3/16 = 0.187
2) net sales amount – 61.30/274.36 = 0.223
3) age – 18/58 = 0.310
Are there any outlier values of (a) number of items purchased, (b) net sales amount, and (c) customer age in the sample data (yes or no)? If yes, state the specific value or values which are the outliers.
Yes.
a) For # items 6 outliers are identified with values 9, 10, 13 and 17
b) For age one outlier identified is with value 78 yrs
c) For net sales amount 5 outliers are identified with values $ 198.80, 229.50, 253, 266 and 287.59
Would you recommend using the midrange as an approximation for the expected (a) number of items purchased, (b) net sales amount, and (c) customer age? Briefly state why for each.
Mid range can be used as an approximation for the customer age but not for # items and net sales amount as there is lot of difference between mean and mid range values for # items and net sales.
Clothes R’ Us(Questions 16 to 21, inclusive)
A sample of n = 22 in-store credit card transactions was collected for another TBJD holding, Clothes R’ Us. Sample statistics for the net sales amount have been calculated and the results are reported in the paragraph below.
Per transaction, the mean net sales amount is $64.45 with a standard deviation of $21.15. The median net sales amountis $57.20. The sampled net sales amountshave no mode. The smallest amount is $19.08 and the highest amount is $218.
Generally, how much money is a customer expected to spend at Clothes R’ Us?
Customer is expected to spent $ 118.54.
Is there relatively high or low variability in the sampled net sales amountsforClothes R’ Us? Briefly state why.
Relatively low variability is observed with coefficient of variation of 32.816%.
How strongly should the value reported for question 14 be expected for Clothes R’ Us?
Are the sampled net sales amountsfor Clothes R’ Usskewed or not skewed?If it is skewed, which way?
They are skewed to the right with mean greater than median.
a. Are there any outliers in the sample of net sales amounts for Clothes R’ Us?
If yes, which specific value or values are the outliers?
Are the values identified in part b outliers for XYZ Apparel?
Comparison of XYZ ApparelandClothes R’ Us (Questions 22 to 25, inclusive)
Suppose a customer spends $65.87.
For XYZ Apparel:
Would this be about expected or unexpected?
About unexpected
Would this be a high or a low amount?
We will test it through z-test –
x=$65.87, µ = 77.60, σ = 55.66, n =100
z = (x-µ)/σ/√n = (65.87-77.60)/55.66/10 = -2.11
From z-table,
p(z) = p(-2.11) = .0174
As v alue is less than mean so this is a Low amount.
Would this be usual or unusual?
As the p-value is less than 0.05 level of significance so this is an unusual case.
For Clothes R’ Us:
Would this be about expected or unexpected?
Unexpected.
Would this be a high or a low amount?
We will test it through z-test –
x=$65.87, µ = 64.45, σ = 21.15, n =22
z = (x-µ)/σ/√n = (65.87-64.45)/21.15/√22 = 0.315
From z-table,
p(z) = p(0.315) = .6217
As value is greater than mean so this is a high amount but still comparable to mean.
Would this be usual or unusual?
As the p-value is greater than 0.05 level of significance so this is an usual case.
Which of the two data samples for net sales amount is more variable, the one forXYZ Apparel or the one for Clothes R’ Us? Briefly state why.
XYZ apparel as CV value is 71.73% which is quiet high as compared to low CV for Clothes R’ Us (32.82%)
Which of the two clothing companies, XYZ Apparel or Clothes R’ Us, is generally more reliable as regards net sales amount? Briefly state why.
Clothes R’ Us because it is less variable and the diffrenec between mean and median is also less.
a. On average, which of the clothing companies, XYZ Apparel or Clothes R’ Us, is expected to have a highernet sales amount per transaction?
XYZ Apparel
On average, how much higher is the expected net sales amount?
$ 31.87
Frequency Description for theXYZ Apparelsample (Questions 26 to 30, inclusive)
Present below a frequency and relative frequency distribution for the net sales amounts for XYZ Apparel. Use the methodology presented and demonstrated in class.
|
Class |
frequency |
percent |
|
0-20 |
4 |
4.0 |
|
20-40 |
22 |
22.0 |
|
40-60 |
25 |
25.0 |
|
60-80 |
16 |
16.0 |
|
80-100 |
7 |
7.0 |
|
100-120 |
10 |
10.0 |
|
120-140 |
2 |
2.0 |
|
140-160 |
6 |
6.0 |
|
160-180 |
2 |
2.0 |
|
180-200 |
2 |
2.0 |
|
200-220 |
0 |
0.0 |
|
220-240 |
1 |
1.0 |
|
240-260 |
1 |
1.0 |
|
260-280 |
1 |
1.0 |
|
280-300 |
1 |
1.0 |
Present below the relative frequency histogram of net sales amount according to your distributions in part 23.
On the basis of the distribution you made above in part 23:
a. Is this distribution skewed or not? If it is skewed, which way?
Skewed to the right
Is your conclusion in question25.aconsistent with your result stated inquestion10? (Pick either yes or no.) If it’s not, explain why.
Yes
In general, as a class range of money, how much money is most typically spent at XYZ Apparel?
$ 40-60
As a percentage, generally how typical is this most typical range?
25%
Overall
What assumptions did you have to make about the samples drawn for XYZ Apparel and for Clothes R’ Us to come to all of your conclusions so far on this exam.
The data collected is random sampled and is normally distributed.
(NEnd of Exam 1)
References:
1) A Measure of Relative Variability. Available from: https://www.medialabinc.net/spg131067/a_measure_of_relative_variability.aspx [accessed on 19/02/2015]
2) Relative Frequency. Available from: https://www.mathsisfun.com/data/relative-frequency.html [accessed on 19/02/2015]
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