BCO127 Applied Management Statistics Assignment: Analysis & Solutions

This document presents a comprehensive solution to an Applied Management Statistics assignment. The solution addresses several key statistical concepts, including identifying populations and appropriate sampling methods for a study on Barcelona's transportation system, calculating and interpreting confidence intervals for mean delivery times in an e-commerce context, analyzing regression models to determine relationships between variables like work experience and annual income, and explaining the process of sample selection using random numbers to avoid bias. The assignment covers topics such as hypothesis testing, confidence intervals, regression analysis, and sampling techniques, providing detailed explanations and interpretations of the results obtained. The solution utilizes statistical methods to analyze data and draw meaningful conclusions relevant to the assignment's objectives. References to relevant statistical literature are also included.

Running head: APPLIED MANAGEMENT STATISTICS
Applied Management Statistics
Name of the Student
Name of the University
Course ID

1APPLIED MANAGEMENT STATISTICS
Table of Contents
Question 1........................................................................................................................................2
Question a....................................................................................................................................2
Question b....................................................................................................................................2
Question 2........................................................................................................................................2
Question a....................................................................................................................................2
Question b....................................................................................................................................2
Question c....................................................................................................................................3
Question d....................................................................................................................................3
Question 3........................................................................................................................................4
Question a....................................................................................................................................4
Question b....................................................................................................................................4
Question 4....................................................................................................................................4
Question a....................................................................................................................................4
Question b....................................................................................................................................5
Question c....................................................................................................................................5
Question d....................................................................................................................................5
Question 5........................................................................................................................................5
References........................................................................................................................................7

2APPLIED MANAGEMENT STATISTICS
Question 1
Question a
The population in the study is all the students in the Applied Management Statistics class.
Question b
Simple random sample can be used for this purpose because in that all the students have
an equal chance of appearing in the sample and express their opinion. This would make the
sample unbiased (Ross 2017).
Question 2
Question a
95 % confidence interval=x ± tα
2
× s
√n
¿ 4 ±2.0639 × 1.2
√ 25
¿ 4 ± ( 2.0639 × 0.2400 )
¿ 4 ±0.4953
¿ 3.50 , 4.50
Question b
Null hypothesis ( H0 ) : μ=3
Alternative Hypothesis ( H1 ) : μ<3

3APPLIED MANAGEMENT STATISTICS
Question c
Table 1: Result of test for mean
Null Hypothesis μ = 3
Alternative Hypothesisμ < 3
Test Type Lower
α 0.05
24
-1.7109
1.7109
1.2
4
25
0.2400
4.1667
0.0003
Reject Null Hypothesis
Standard Error of the Mean
t Sample Statistic
p-value
Decision
Lower Critical Value
Upper Critical Value
Sample Data
Sample Standard Deviation
Sample Mean
Sample Size
Hypothesis Test for μ
Hypotheses
Level of significance
Critical Region
Degrees of Freedom
Question d
The test result suggests rejection of null hypothesis that mean delivery time is days. This
in turn means acceptance of alternative hypothesis that mean delivery time is less than 3 days
(Pearl, Glymour and Jewell 2016). Therefore, the manager’s claim that mean delivery time of
their products does not exceed 3 days is true.

4APPLIED MANAGEMENT STATISTICS
Question 3
Question a
99 % confidence interval=x ± Z α
2
× σ
√n
¿ 28 ± 2.58× 5
√100
¿ 28 ± ( 2.58× 0.5 )
¿ 28 ±1.29
¿ 26.71 ,29.29
Question b
From the 99% confidence interval estimate it can be concluded with 99% confidence that
mean hours of kids watching television time lies between 26.71 hours and 29.29 hours.
Question 4
Question a
For the given model annual income in likely to be the dependent variable and work
experience is likely to be the independent variable. Annual income is likely to be positively
associated with work experience indicating a positive correlation between them. This is further
supported from the regression result having a value of correlation coefficient of 0.93 suggesting
a strong positive association between them (Schroeder, Sjoquist and Stephan 2016).

5APPLIED MANAGEMENT STATISTICS
Question b
The R square value is 0.86. The R square value is interpreted as the proportion of
variation of the dependent variable as accounted by the independent variable. From the R square
value, it can be said that work experience accounts for 86 percent variation of income.
Question c
Regression model,
Annual Income=17351+(1362× Work Experience)
Value of the coefficient of work experience is 1362. The coefficient is positive meaning
that work experience has a positive influence on income. That is income increases with increase
in years of work experience (Darlington and Hayes 2016). More accurately, with 1-year increase
in work experience average income increases by 1362 thousand euro.
Question d
Estimated annual income with a work experience of 15 years,
Annual income=17351+ ( 1362×15 )
¿ 17351+20430
¿ 37781
Question 5
Total number of smart phones given for sample selection is 293. In order to keep the
sample unbias, sample selection process considers random numbers up to first 3 multiples of
293. In that, all the observation has 3 equal chance of being selected in the sample. For selecting

6APPLIED MANAGEMENT STATISTICS
sample, from the random number table three digit numbers are selected by following horizontal
sequence. We begin from row 05 and column 11 of the random number table. If the selected
random number comes out to be larger than 293 but smaller than 586 (2nd multiplier) then 293 is
subtracted to get the desired serial number. If the random number is between second and third
multiple of 293 then 586 is subtracted from the number to get the serial number of the sample.
Similarly, if the random number is between third and fourth multiple of 293 then 879 is
subtracted from the random number. For example, the first number obtained from the random
number table is 514 which is greater than 293 but less than 586. Therefore, 293 is subtracted
from it and the desired serial number for the sample is (514 – 293) = 221. This process continues
unless 10 numbers are obtained get the desired set of sample.
Table 2: Sample data

7APPLIED MANAGEMENT STATISTICS
References
Darlington, R.B. and Hayes, A.F., 2016. Regression analysis and linear models: Concepts,
applications, and implementation. Guilford Publications.
Pearl, J., Glymour, M. and Jewell, N.P., 2016. Causal inference in statistics: A primer. John
Wiley & Sons.
Ross, S.M., 2017. Introductory statistics. Academic Press.
Schroeder, L.D., Sjoquist, D.L. and Stephan, P.E., 2016. Understanding regression analysis: An
introductory guide (Vol. 57). Sage Publications.