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Running head: STA-201: PRINCIPLES OF STATISTICS 1
Sta-201: Principles of Statistics I
Student Name
Institution
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STA-201: PRINCIPLES OF STATISTICS 2
Introduction
The roles of Production managers in manufacturing companies is determining whether it
is economical to produce a variety of products with the condition of maximizing the profits while
minimizing the inputs. These inputs are not limited to the capital, human labor, and the right
product mix. Production companies which produce a variety of products, carry out a product mix
to understand the right quantities of production for each product. Producing the right quantities
of products maximizes the company’s returns (Taha, 2017). Therefore, determining the right
product mix is essentially important for profit maximization and growth of a firm or an
institution.
Background of the Study
Human beings look alike, regardless of age and gender. Humans have equally similar
body characteristics such as two eyes, two legs, two hands, and one head. Moreover, most human
beings dress and wear a pair of shoes at a time. Nyke Limited is a shoe manufacturing company
which produces a variety of shoe products to meets its customer's needs and expectation. Nyke
shoes are designed to meet the needs and the expectations of customers of all gender, age,
client’s height.
Producing a variety of shoe product is time-consuming, and expensive compared to the
production of one shoe size. Nyke Shoe limited wishes to manufacture just one type of shoe for
all their customers to cut down the cost of production and maximize returns.
Initially, Nyke Shoe Company produced a variety of shoes for different gender, age, and height
of its customers. However, the company is facing financial difficulties at the moment and intends
to seek expert advice on whether it is worth making only one shoe size for all gender irrespective
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STA-201: PRINCIPLES OF STATISTICS 3
of the height of a person. Therefore, this paper employs statistical tools in determining whether it
is the best plan for Nyke to product just the same shoe size for all the customers.
Hypothesis Statement
Hypothesis 1
𝐻
0
: No correlation between shoe sizes and the height
𝐻
𝑎
: There is a significant correlation between shoe sizes and the height
Hypothesis 2
𝐻
0
: The fitted regression model between shoe size and height is not statistically significant
𝐻
𝑎
: The fitted regression model between shoe size and height is statistically significant
Hypothesis 3
𝐻
0
: The shoe size to height ratio for a male is equal shoe size to height ratio for female
𝐻
𝑎
: The shoe size to height for male ratio and the shoe size to height for the female ratio is
different
Data
The relevance, validity, and reliability of the collected sample data are key determinants
of a good statistical study (Spiegel & Stephens, 2011). Moreover, data collection techniques
determine the accuracy of the collected data. This study utilizes secondary data from Nyke Shoe
Company. Nyke Shoe Company provided a sample size of thirty-five customer data. The sample
data consisted of three variables; shoe size, height, and gender of their customers. Logically, a
sample data size of 35 from a shoe production company is little based on the average number of
shoes produced by Nyke Shoe Company. However, the sample size (N=35) is greater than 30;
thus, the data meet the minimum threshold for normality assumption thus can be used for making
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STA-201: PRINCIPLES OF STATISTICS 4
conclusions and recommendations to Nyke shoe company. Lastly, the picking of the thirty-five
sample data was assumed to be random.
Data Analysis
Several statistical tests will be conducted to determine the viability of the sample data to
the research question. First, the descriptive statistics for the three variables (age, gender, and
shoe size) will be calculated. Descriptive statistics such as mean, median, mode, range, variance,
and the standard deviation will be calculated and interpreted. Secondly, the data will be used to
visual graphs such as boxplot, histogram, scatterplot, and stem and leaf diagram. Such graphs
will aid in detecting any outliers in the sampled data and the necessary corrective measures taken
before conducting inferential statistic on the data. Additionally, the scatterplots will assist
determining the skewness of the sample data. Lastly, inferential statistics such as two-sampled t-
test, regression, and correlation study is conducted to test the study hypotheses.
The sampled data is both quantitative and qualitative. The shoe size and age variables are
quantitative while the gender variable is qualitative. For the purposes of data analysis, the
provided data is transferred to Ms-excel spreadsheet for easy and fast data analysis. In order to
achieve all the study objectives, the data was sorted to all shoe sizes, all heights, gender (heights
and shoe size for women only and heights and shoe size for men only). After sorting the data in
these categories, various descriptive statistics will be conducted for all these categories.
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STA-201: PRINCIPLES OF STATISTICS 5
Results and Interpretation
From the above diagram, the mean shoe size is 9.143 (𝑥=9.143) with a standard deviation of
2.582666852 (SD=2.583). Additionally, the minimum and the maximum show size for Nyke
customers are 5 (Min=5) and 14 (Max=14) respectively. Similarly, the mean height for Nyke
customers is 68.94286 (𝑥=68.94286) with a standard deviation of 2.582666852 (SD=4.028887).
Additionally, the minimum and the maximum height for Nyke customers are 5 (Min=60) and 14
(Max=77) respectively.
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STA-201: PRINCIPLES OF STATISTICS 6
From the above diagram, the average male height is 71.35 (𝑥=71.35) with a standard deviation of
3.14 (SD=3.14). Additionally, the minimum and the maximum height for male customers are 64
(Min=64) and 77 (Max=77) respectively. Similarly, the average female height for customers is
66.667 (𝑥=66.667) with a standard deviation of 3.4470789 (SD=3.447). Additionally, the
minimum and the maximum height for female customers are 60 (Min=60) and 72 (Max=72)
respectively.
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