YOYO Case Study 1: Data Analysis and Recommendations for BB's Yo-Yos

This case study presents a statistical analysis of a YOYO product, examining customer feedback and product performance. The analysis begins with an exploration of categorical data using pie charts and chi-square tests to determine the distribution of gender and customer satisfaction levels. Outlier tests were conducted to identify anomalies in the data. Pearson correlation coefficient was used to assess the relationship between YOYO performance and customer satisfaction. Furthermore, regression analysis was performed to determine the impact of various factors, including performance, gender, feel, and weight, on overall customer satisfaction. The findings reveal key insights into customer preferences and provide data-driven recommendations for product improvement, such as enhancing the YOYO's performance and feel.

Running head: YOYO CASE STUDY 1
YOYO Case Study
Name
Institution

YOYO CASE STUDY 2
YOYO Case Study
Statistical Analysis
The analysis begins with exploration of categorical data using pie chart and test for
difference in proportions. The next analysis is based on the colour preferences among boys
and girls followed by test for outliers. The final section includes correlation and regression
analysis.
Analysis of categorical Variables
Figure 1 shows proportion of the sample participants with their respective gender.
From figure 1 the sample seems to over present boys at 59.3% while girls are 40.7%,
however, to verify whether the observed variation is statistically significant, Chi-Square
goodness-of-fit test for categorical variable is performed (Goh, 2017).
Girl
Boy
Category
59.3%
40.7%
Figure 1: Pie Chart of Gender of Participants
The results of the chi-square goodness-of-fit tests are presented in table 1.
Table 1: Test of difference in Proportion in Gender
Gender Observed Test Proportion Expected Contribution
Boy 593 0.5 500 17.298
Girl 407 0.5 500 17.298
Chi-square = 34.596
P-value = 0.000
DF = 1

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The Chi-square statistics for the tests is 34.596 with equal contribution of 17.298 from
both genders and one degrees of freedom. The corresponding p-value for the Chi-square
statistics is 0.000 which is less than significance level of 0.05. Therefore, the genders are not
equally represented verifying that boys are over-represented in the sample. If there exist a
next stage of testing the YOYO product then equal number of boys and girls should engaged
in the final sample. Next, figure 2 shows a pie chart for the customers satisfaction with the
feel of the tests YOYO product.
6
4
5
7
Other
Category
9.3%
28.0%
25.6%
23.7%
13.4%
Figure 2: Pie Chart of Customer Satisfaction with the Feel of BB Yo-Yo
From the figure 2, only 9.3% of the customers did not prefer the feel of the YOYO
while the remaining 90.7% preferred the feel (23.7% level 4 + 25.6% level 5 + 13.4% level 6
+ 28.0% level 7). The scale used is ordinal implying that response of 1 is less than response
of 2, therefore, the median would make sense. In this case the median is response of 4.
Therefore, any response equal and above 4 is considered preferable. Based on these results
the feel of the YOYO is preferred by majority of the customers and this attribute can be used
as a selling point of the product. Next, figure 3 shows pie chart for customers satisfaction
with the weight of the YOYO.

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7
4
6
5
Category
43.3%
43.2%
7.2%
6.3%
Figure 3: Pie Chart of Customer Satisfaction with the Weight of BB-Yo-Yo
Similar to the feel response in figure 2, the customers are satisfied with the weight of
the YOYO since the least satisfaction level assigned by the participants is 4. Therefore, the
weight of the YOYO is satisfactory to the customers hence another selling point for the
product. Figure 4 shows pie chart of customers preference to colour of the YOYO.
Dislike
Like
Category
67.5%
32.5%
Figure 4: Pie Chart of Customer Satisfaction with Color of BB-Yo-Yo
From figure 4, majority of customers like the colour of the YOYO (67.5%) while
32.5% dislike the colour. In order to explore the extent of the dislike compare gender and
colour. Figure 5 shows the bar chart of the gender satisfaction with the colour of the YOYO.

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Gender
Color
GirlBoy
LikeDislikeLikeDislike
40
30
20
10
0
Percent
Percent within all data.
Figure 5: Chart of Gender Satisfaction with Color of BB-Yo-Yo
The figure 5 shows that twenty percent of the boys dislike the colour of the YOYO
while fifteen percent of the girls dislike the colour. Therefore, the colour should be changed
to the liking of the boys to increase customer satisfaction with the colour.
Outlier Test for Overall Satisfaction
The outliers were tested and identified based on Grubbs’ test founded on the
following hypothesis:
Null hypothesis: All data values come from the same normal population
Alternative hypothesis: Smallest or largest data value is an outlier
Significance level α = 0.05
The table 2 shows the results of the Outlier test.
Table 2: Grubbs Outlier Test Results
Gender G-statistic P-value Outlier Row Outlier value
Boy 4.10 0.022 20 0
Girl 4.28 0.006 81 0
In both cases (boys and girls) the p-value for the Gibbs statistics are less than
significance level α = 0.05, hence reject the null hypothesis in favor of the alternative
hypothesis and conclude that there exists an outlier in the overall satisfaction variable. For the

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boys the outlier is in YOYO serial number 20 and the value is zero while for the girls the
outlier is in YOYO serial number 81 with a value of zero. In order to find out the correlation
between performance of the YOYO (spinning rate) and customers overall satisfaction,
Pearson correlation coefficient was obtained. The analysis gave r = 0.374 with a
corresponding p-value of 0.000. Thus, implying that there exists a weak positive correlation
between performance and overall satisfaction. Further, the correlation is significant since the
p-value is less than significance level of 0.05. Therefore, to improve sales of YOYO in the
market improvements should be focused on its performance (spinning rate).
Regression Analysis of the Customers Satisfaction
Table 3 shows the regression output with overall satisfaction as the response variable.
In the analysis only gender and color were treated as categorical data since the averages of
feel, and weight makes sense, hence used as continuous predictors.
Table 3: Regression results
Term Coefficient SE t-value P-value
Performance 0.5668 0.0350 16.19 0.000
Gender 12.99 1.11 11.74 0.000
Feel 0.982 0.367 2.67 0.008
Weight 5.791 0.459 12.62 0.000
Color 0.54 1.17 0.46 0.645
The constant term was not included in the regression because it would not make sense
(there is no YOYO with zero weight) (Lesik, 2018). The coefficients of performance, gender,
feel, and weight are having t-statistics with p-values less than significance level of 0.05.
Therefore, the customers satisfaction with the YOO product is affected by performance,
gender, feel and weight.
Satisfaction = 0.5668 Performance + 0.982 Feel + 5.791 Weight (1)
From equation (1 -4), one percent improvement in performance of YOYO would
increase the level of satisfaction by an average percentage of 0.5668. Next, an improvement
in the feel of the YOYO would increase their satisfaction with the product by an average of

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0.982 percent. Finally, a unit increase in the weight of YOYO would improve the overall
satisfaction by an average of 5.791 percent.

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References
Goh, T. N. (2017). Conventional Analysis with Categorical Data from a Statistically
Designed Experiment. Quality and Reliability Engineering International, 33(5), 1143-
1147.
Lesik, S. A. (2018). Applied Statistical Inference with MINITAB®. Chapman and Hall/CRC.