Assignment 2
[School]
Question 1
a. Excel generated the histograms for this question. The histogram plots are as follows:
b. Using the 1.5XIQR rule for the three scores:
Donating Money: 24×1.5=36→Q1-36=-22;Q3+36=74
The “Donating Money” score has three outliers. These three are all exceptionally high ( > 74). The scores are 77, 78 and 91.
Helping a Stranger: 17.5×1.5=26.25→Q1-26.25=13.75;Q3+26.25=83.75
Volunteering Time: 16×1.5=24→Q1-16=-11;Q3+16=53
The scores “Helping a Stranger” and “Volunteering Time” do not have outliers.
c. Donating Money: The distribution for Donating score is positively skewed, tailing to the right. There are 3 outliers observed; the values of these outliers are 77, 78, and 91. The bulk of the distribution is located at the lower values, and a larger tail is observed at the higher values. Helping a Stranger: The distribution closely resembles a standard normal distribution (the shape is bell-shaped). There are no outliers observed in this score. The tails for both the high and the low ends are similar, and the bulk of the distribution is evenly distributed.
Volunteering Time: The distribution is positively skewed with a tail trailing to the right. There are no outliers observed. The boxplots show no outliers and a bigger tail on the higher values compared to the lower values.
Central Tendency and Dispersion: The most appropriate measure of central tendency is mean, while the most appropriate measure of dispersion is the variance. The mean is the best measure to compare the three scores because they are all quantitative in nature, and the variance is the best measure of dispersion because of the same reason.
d. Interpretation of Results: Higher efforts are observed in “Helping a Stranger” because of the high mean and sum of the scores. In contrast, the least efforts are observed in “Volunteering Time” because of the low mean and sum of the scores. In “Donating Money”, although the mean is quite low, there are 3 exceptionally high scores that cannot be ignored. Based on the means of the scores, Australia performs above average on all the methods of giving.
Question 2
a. 100% Stacked Column Chart:
b. Fundraisers:
P(F)=No. of FundraisersTotal=2761570=0.176
c. i. Generation Y: P(Y)=Generation Y FundraisersTotal Fundraisers=70276=0.254
ii. Generation X: P(X)=Generation X FundraisersTotal Fundraisers=76276=0.275
iii. Baby Boomers: P(BB)=Baby Boomer FundraisersTotal Fundraisers=85276=0.308
iv. Matures: PM=Mature FundraisersTotal Fundraisers=45276=0.163
d. Mobile:
P(Mo)=No. of Mobile ParticipantsTotal=1441570=0.092
i. Generation Y: P(Y)=Generation Y MobileTotal Mobile=54144=0.375
ii. Generation X: P(X)=Generation X MobileTotal Mobile=42144=0.292
iii. Baby Boomers: P(BB)=Baby Boomer MobileTotal Mobile=43144=0.299
iv. Matures: P(M)=Mature MobileTotal Mobile=5144=0.035
e. Access to technology is observed to be a critical criterion in how the different generations participate in charity. The “Mail” way is observed to be used more by the more mature generations, and the numbers decrease as the generations get younger. The “Mobile” way is observed to be used more by the younger generations, and the numbers decrease as the generations get older. Generation X has the most number of “Workplace” participants mainly because most of the people in this generation are in the working class. The “Fundraiser” way is most preferred by Generation Y.
Question 3
a. Decision Variables: number of radio spots (R), number of flyers (F), number of newspaper ads (N)
Objective: Maximize the number of audience reached
The objective function is Maximize Audience= 5000R+2400F+2800N
Constraints:
Total Expenses: 800R+240F+320N≤8000
Print Ads Expenses: 240F+320N≤2400
Total Number of Print Ads: F+N≥5
b. Excel Solver Output
c. The optimal number of radio spots is 7; the optimal number of flyers is 10; the optimal number of newspaper ads is 0. All these optimal values did not reach the maximum constraints; the non-negativity constraints are all satisfied. Therefore, the shadow prices cannot be analyzed with the given results.
d. Total Expenses = $12000. The Excel Solver output is:
The optimal number of radio spots increases to 12, which is the maximum constraint for radio spots; the other variables stayed constant. This change resulted to an increase in the number of audience reached. (59000→84000).
e. Total Print Ads Expenses = $6500. The Excel Solver output is:
The optimal values are R=2, F=24, and N=2; the number of audience reached is 73200. The number of flyers dramatically increased from the original.
f. Recommendations for Joey
In the present state of expense allocation, increasing the budget definitely increases the number of audience reached. For a fixed budget, increasing the allocation towards the print advertisements (particularly the flyers) rather than the radio spots guarantees an increase in the number of audience reached.
Question 4
a. Scatterplot of Website Data:
A trend is observable in which the number of on-line orders increases as the number of unique visits increases. The increase is steady but is apparent in the whole range of values. It is appropriate to fit a regression line because of this observed trend.
b. Scatterplot of Website Data with Regression Line:
The intercept is very near zero, which just right because for zero unique visits, there should also be zero on-line orders. The slope is much less than 1, but is positive, which verifies the steady increasing trend. The coefficient of determination is very near 1, making the regression equation an accurate model of the scatter data.
c. Regression Line Equation: y=0.0752x+0.795
Unique Visits x, On-line Orders y: If x=80000,
On-line Orders y=0.0752x+0.795=0.075280000+0.795=6016
Conversion Rate: 601680000=0.0752→752 online orders per 10000 unique visitors
The conversion rate simply went back to the value of the slope of the regression line. This validates the accuracy of the prediction; if the number of visitors is large, the effect of the intercept value (0.795) in the equation is negligible. Thus, the slope of the regression line is the conversion rate.
d. Interpretation of Results: The number of online orders is directly proportional to the number of unique visits in a period of time. This means that if the number of unique visits is high, the number of online orders is expected to be high, with conversion rate of: 752 online orders per 10000 unique visitors.
