Business Statistics

This document discusses various aspects of Business Statistics, including the relation between pay for version 1 and 2, consumer preferences, hypothesis testing, and more. It provides insights into the statistical analysis and interpretation of data in the context of business decision-making.

Running head: BUSINESS STATISTICS
Business Statistics
Name of the Student
Name of the University
Author Note

1BUSINESS STATISTICS
Part a
My sample number is 53
summary, in the assignment you will have to get these
values yourself using a pivot table.
xbar1 xbar2 s1 s2 n1 n2
1004.38 1085.55 123.246 120 21 29
The above table presents the relation of region and how much would consumers pay for
version 1.
It can be interpreted from the above table that consumers would pay average $1085.55 for
version 1 from region B which is higher than from region A (average $1004.38)
The number of consumers interviewed from region B is 29 while from region A is 21. Total
50 consumers were interviewed. The standard deviation of how much consumers would pay
for version 1 from region B is $120. The standard deviation of how much consumers would
pay for version 1 from region A is $213.246

2BUSINESS STATISTICS
Part b
$800 $900 $1,000 $1,100 $1,200 $1,300 $1,400
$600
$700
$800
$900
$1,000
$1,100
$1,200
f(x) = − 1.00770765459315 x + 1979.04429049851
R² = 0.988933906725072
Relation between pay for version 1 and 2
How much would they pay for version 1
ow much would they pay for version 2
Figure 1 represents the relation between how much consumers would pay for version
1 to how much consumers would pay for version 2.
The relation is expressed as:
How much consumers would pay for version 2 = 1979 – 1.0077*How much consumers
would pay for version 1
Thus it is found that as consumers pay higher for version 1, it would decrease for consumers
paying for version 2. Thus with increase in pay for version 1 there is a decrease in pay for
version 2.

3BUSINESS STATISTICS
Part c
n y total
A count 8 13 21
A % 38.10% 61.90% 100.00%
B count 7 22 29
B % 24.14% 75.86% 100.00%
total 15 35 50
From the 50 consumers surveyed 35 would pay higher for version 1 as compared to
15 who disagreed to pay higher for version 1. 75.86% of all consumers surveyed from region
B would pay higher for version 1. 61.90% of all consumers surveyed from region A would
pay higher for version 1.
Part d
The formula to calculate 95% CI would you pay higher for version 1: ^p+ z0.95 √ ^p (1− ^p)
n
Where ^p = 0.70
n = 50
z0.95= 1.96
Thus,
The upper boundary = 0.70+1.96∗
√ 0.70 ( 1−0.70 )
50 =0.827023
The lower boundary = 0.70−1.96∗ √ 0.70 ( 1−0.70 )
50 =0.665666

4BUSINESS STATISTICS
Part e
To test the test statistics that consumers would pay more than $1000 for version 1
x = 1051.46
μ = 1000
σ = 126.58
n = 50
The formula:
The test statistics z= x−μ
σ
√ n
= 1051.46−1000
126.58
√ 50
= 51.46
17.9 =2.87
Part f
Estimate
xbar1-xbar2
-81.1708
standard error of estimate xbar1-xbar2
34.8873
t test stat df two sided pvalue
-2.32666 42 0.02488
To calculate the p-value H0:μ1=μ2 is assumed to be
true
since the test is two sided H1 is H1:μ1≠μ2
From the above table p-value = 0.02488

5BUSINESS STATISTICS
p-value is less than 0.05
Therefore, at 5% level of significance, we reject the null hypothesis. Thus μ1 ≠ μ2. Thus
consumers of region B would pay higher than that of region A.
Part g
pvalue and test stat calculation, you will need to paste this into the Estimate
n1 n2 phat 1 phat 2
phat1 -
phat2
21 29 0.61905 0.7586207 -0.139573
Estimate of the difference between sample proportions
-0.13957
standard error of
estimate test stat two sided pvalue
0.131306 -1.062956837 0.2878015
To calculate the p-value H0:p1=p2 is assumed to be true
since the test is two sided H1 is H1:p1≠p2
From the above table p-value = 0.2878015
p-value is more than 0.05
Therefore, at 5% level of significance, we do not reject the null hypothesis. Thus p1= p2.
Part h
Laptops today form an essential equipment. Various factors are considered by
consumers when purchasing laptops. The business house can consider some of these factors
in order to study consumer preferences.
An essential factor considered when purchasing a laptop is the speed of the laptop.
The speed of a laptop is measured in RAM. The higher the RAM in a laptop the higher is its
processing speed. The business house can collect information on the preferred processing

6BUSINESS STATISTICS
speed of a laptop. The price of a laptop depends on the processing speed. The information can
be collected as a numerical variable. The numbers signifying the speed of laptop.
Screen size is another factor which influences the purchase of a laptop. The higher the
screen size the bigger the laptop. Increase in size of the laptop means that it is heavier also.
Laptops screens have a typical size range from 12-inch to 17-inchs. Since laptops are portable
equipment’s, hence most of the consumers may prefer smaller screens. Still others may prefer
to use a large screen laptop. Thus the response to the screen size would be a numerical
variable.
A third factor which the business organization can consider is the brand of the laptop.
Laptops today are manufactured by different organizations. Consumers may have their
preferences towards a particular brand. Thus the brand names would form the responses to
the questions – which brand do you prefer? Hence we find that the brand of the laptop is a
qualitative variable.
Another question which the business may ask the consumers is the choice of
processors. Most laptops today have either of i3, i5 or i7 processors from Intel. Thus the
business house may ask the consumer his choice of processor. The response would be a
categorical variable.
We find that their various questions which might be asked to the consumers of the
business organization. The response may be a quantitative or a qualitative response.
Part i
A study between two variables is usually to understand the cause-and-effect between
the variables. In the study one of the variables is the independent variable. This variable does
not depend on any other factor. However, the second variable depends on the independent
variable. The second variable is termed the response variable. Information (data) for the two

7BUSINESS STATISTICS
variables are usually collected to uncover the relationship between the variables. In such a
study sometimes it so happens that a third variable has a confounding effect on both the
variables. This third variable is known as a lurking variable.
For example, a research wanted to find the relationship between diet and blood
pressure. The research question framed was does blood pressure f an individual depend on his
diet. The relation between diet and blood pressure can be found from the above experiment.
However, blood pressure does not solely depend on diet. Other factors like stress, life styles,
age have been found to affect blood pressure. Thus these other factors in the experiment are
termed as lurking variables.
Previously we studied the relationship between “would you pay higher for version 1
and version 2.” In the study “would you pay higher for version 1” is the independent variable
and “would you pay higher for version 2” the dependent variable. The relation was defined
through an equation. This type of relation is known as cause and effect relation. In the study
“would you pay higher for version 2” depended on other factors also apart from “would you
pay higher for version 1” then those variables would be known as “Lurking variables.”
In the above study we find that r2 = 0.9889.
Then the influence of lurking variable in predicting “would you pay higher for version
2” = 1-0.9889 = 0.0111.
Part j
A report generally consists of three sections – an introduction section, body of the
report and a concluding section.
In the introductory section, we can provide an overview of what we would be doing in
this report. We in the present assignment studied the relation between two variables. We

8BUSINESS STATISTICS
studied how to relate a categorical and a numerical variable. We also studied the relationship
between two numerical variables. And lastly we studied the relationship between two
categorical variables.
In the body of the report we discuss the methods by which we study the relationship
between the variables. In “answer a” we evaluate the relationship between a categorical
variable and a numerical variable. Statistical processes of average, standard deviation and
count are used to study the relationship. In “answer b” we study the relationship between two
numerical variables. Scatter plot is used to study the relationship of how the independent
variable influences the dependent variable. Regression analysis is used to evaluate the
relationship. In this section we also study of what is a lurking variable and it influences the
dependent variable. In “answer c” we study the relationship between two categorical
variables. Cross tabulation is used to study the relationship between the two variables.
Confidence interval is used to study a numerical variable in “answer d.” In answers “e, f and
g” we used inferential statistics to find the relationship between two variables.
The concluding part should mention what we learned from the above studies. We
from the above study learnt that in any statistical we should first evaluate the variables
through the use of descriptive statistics. Thereafter relation between two variables can be
studied. Relationship between two variables through inferential statistics. Usually t-test is
used to test the relationship between two variables. Confidence interval is an effective
method to study a numerical variable.

9BUSINESS STATISTICS