Statistics for Business Decisions - Desklib

This document covers topics like ANOVA, regression analysis, histograms, and more related to Statistics for Business Decisions. It includes solved assignments, essays, and dissertations. The content is relevant for students pursuing courses in business and statistics.

Running Head: STATISTICS FOR BUSINESS DECISIONS
Statistics for business decisions
Name of the Student
Name of the University
Author Note

1STATISTICS FOR BUSINESS DECISIONS
Table of Contents
ANSWER 1.....................................................................................................................................2
Part a............................................................................................................................................2
Part b............................................................................................................................................2
Part c............................................................................................................................................3
ANSWER 2.....................................................................................................................................3
Part a............................................................................................................................................3
Part b............................................................................................................................................3
Part c............................................................................................................................................3
ANSWER 3.....................................................................................................................................4
ANSWER 4.....................................................................................................................................4
Part a............................................................................................................................................4
Part b............................................................................................................................................4
Part c............................................................................................................................................5
Part d............................................................................................................................................5
Part e............................................................................................................................................5

2STATISTICS FOR BUSINESS DECISIONS
ANSWER 1
Part a
Class Interval Frequency
Relative
Frequency
Percentage
Relative
Frequency
< 150 3 0.06 6%
150 - 200 15 0.3 30%
200 - 250 14 0.28 28%
250 - 300 6 0.12 12%
300 - 350 4 0.08 8%
350 - 400 3 0.06 6%
400 - 450 3 0.06 6%
450 - 500 2 0.04 4%
The frequency, relative frequency and percentage relative frequency of the value of the
orders is depicted above.
Part b
< 150 150 - 200 200 - 250 250 - 300 300 - 350 350 - 400 400 - 450 450 - 500
0%
5%
10%
15%
20%
25%
30%
35%
Distribution of Value of Orders ($)
Class Interval
Percentage Relative Frequency
A histogram using percentage frequency of the value of the orders is presented above.

3STATISTICS FOR BUSINESS DECISIONS
The shape of the histogram is right skewed. When a histogram is right skewed then median is
less than the mean value of the orders.
Part c
From the above histogram it can be interpreted that the median is less than the mean of the
orders. The median value of the order would segregate the data set into two equal halves such
that the number of orders below and above the value would be similar.
ANSWER 2
Anova
df SS MS F Sig
Regressio
n 1 5048.818 5048.818 74.137 0.000
Residual 46 3132.661 68.101
Total 47 8181.479
Coefficients Standard Error t stat p-value
Intercept 80.39 3.102 25.916 0.000
X -2.137 0.248 -8.617 0.000
Part a
In order to relate the demand and unit price the F-value of the ANOVA table and its significance
is used. From the table it is found that Sig < 0.000 at 0.05 level of significance.
Hence, there is a statistically significant relationship between demand and unit price.
Part b
Coefficient of determination R2 is calculated as ¿ SSM
SST = 5048.818
8181.479 =0.617
R2 = 0.617.

4STATISTICS FOR BUSINESS DECISIONS
Hence, 61.7% in the variation in demand (Y) can be explained from Unit Price (X).
Part c
Coefficient of Correlation R is calculated as ¿ √ R2= √0.617=0.786
R = 0.786.
Hence, the correlation between Demand (Y) and Unit Price (X) is very strong.
ANSWER 3
ANOVA
Source of Variation
Sum of
Squares
Degrees of
Freedom Mean Square F Sig
Between Treatments 390.58 2 195.29 25.891 0.000
Within Treatments
(Error) 158.40 21 7.54
Total 548.98 23
In order to check for significant differences between means
Null Hypothesis: There is no difference between the means of the three populations
Alternate Hypothesis: There are difference between the means of the three populations
Decision: Reject Null Hypothesis if p-value is less than
 = 0.05
From calculations it is found that p-value for the test is < 0.000. Hence we reject the null
Hypothesis Thus it can be inferred that there are statistically significant differences between the
three populations at 0.05 level of significance.

5STATISTICS FOR BUSINESS DECISIONS
ANSWER 4
ANOVA
df SS MS F Sig
Regressio
n 2 40.700 20.350 100.148 0.000
Residual 5 1.016 0.203
Total 7 41.716
Coefficients
Standard
Error t-stat p-value
Intercept 0.8051
X1 0.4977 0.4617 1.078 0.330
X2 0.4733 0.0387 12.230 0.000
Part a
The estimated regression Equation:
 Y = 0.8051 + 0.4977*X1 + 0.4733*X2
Part b
Null hypothesis: There is no significant relationship between the independent variables and
dependent variables
Alternative hypothesis: There is a significant relationship between the independent variables and
dependent variables
Decision Rule: Reject null hypothesis is sig > 0.05
From calculations it is found that p-value for the test is < 0.000. Hence we reject the null
Hypothesis Thus it can be inferred that there is statistically significant relationship between the
independent and dependent variables.

6STATISTICS FOR BUSINESS DECISIONS
Part c
To test if the coefficients are significantly different than zero
Null Hypothesis: The Coefficient of the independent variable (X1) is equal to zero
H0 : β1=0
Alternate Hypothesis: The Coefficient of the independent variable (X1) is more than zero
H1 : β1 >0
Decision Rule: Reject null hypothesis is p-value is > 0.05.
From calculations it is found that p-value for coefficient X1 = 0.330. Hence we do not reject the
null Hypothesis. Thus, the coefficient of X1 is equal to zero.
Null Hypothesis: The Coefficient of the independent variable (X2) is equal to zero
H0 : β1=0
Alternate Hypothesis: The Coefficient of the independent variable (X2) is more than zero
H1 : β1 >0
Decision Rule: Reject null hypothesis is p-value is > 0.05.
From calculations it is found that p-value for coefficient X2 < 0.000. Hence we reject the null
Hypothesis. Thus, the coefficient of X2 is not equal to zero.
Part d
The slope coefficient for X2 is 0.4733.

7STATISTICS FOR BUSINESS DECISIONS
The value of the coefficient can be interpreted as keeping X1 constant, for unit increase in value
of X2 there would be an increase in value of Y by 0.4733.
Part e
The price of one mobile phone X1 = $20 (000)
The number of advertising spots X2 = 10
 Y = 0.8051 + 0.4977*X1 + 0.4733*X2
 Y = 0.8051 + 0.4977*20 + 0.4733*10 = 15.4921
The number of mobile phones the company expects to sell = 15.4921