BCO127 Applied Management Statistics: Statistical Analysis Assignment

This assignment solution addresses various statistical concepts within the realm of applied management. It begins by identifying the population and appropriate sampling methods for a study on college students' opinions regarding Barcelona's transportation system. The solution then delves into hypothesis testing and confidence intervals, analyzing delivery times for an e-commerce company and determining if the manager's claims are valid. Furthermore, it explores confidence intervals related to the mean watching time of kids. The assignment also includes a regression analysis, determining the relationship between work experience and annual income, providing the regression equation and calculating predicted income based on years of experience. Finally, the solution demonstrates how to generate a random sample of mobile phones from a given list, adhering to specific conditions for sample selection. The bibliography lists all resources used for this assignment.

Running head: APPLIED MANAGEMENT STATISTICS
Applied Management Statistics
Name of the Student:
Name of the University:
Author note:

1APPLIED MANAGEMENT STATISTICS
Table of Contents
Answer to the question 1............................................................................................................2
Part (a)....................................................................................................................................2
Part (b)....................................................................................................................................2
Answer to the question 2............................................................................................................2
Part (a)....................................................................................................................................2
Part (b)....................................................................................................................................2
Part (c)....................................................................................................................................3
Part (d)....................................................................................................................................3
Answer to the question 3............................................................................................................4
Part (a)....................................................................................................................................4
Part (b)....................................................................................................................................4
Answer to the question 4............................................................................................................5
Part (a)....................................................................................................................................5
Part (b)....................................................................................................................................5
Part (c)....................................................................................................................................5
Part (d)....................................................................................................................................6
Answer to the question 5............................................................................................................6
Bibliography...............................................................................................................................8

2APPLIED MANAGEMENT STATISTICS
Answer to the question 1
Part (a)
The population of the study is College students.
Part (b)
The study on transportation system in Barcelona different department student has
been taken as a sample. By using stratified random sampling the sample observations has
been selected. Also each and every department has been taken as a strata and by lottery
method of simple random sampling a limited percentage of students are selected for sample.
Answer to the question 2
Part (a)
The number of observations (n) = 25
Mean = 4
Standard deviation = 1.2
The 95% confidence interval for the mean delivery time is
Mean ±1.96 * (standard deviation / sqrt (n))
= 4±1.96 *(1.2/ sqrt (25))
= (3.53, 4.47)
3.53 ≤ meandelivery time ≤ 4.47
Part (b)
Null hypothesis: The delivery time of the product does not exceed 3 days.
Alternative hypothesis: The delivery time of the product is exceed 3 days.

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T-test output
Part (c)
The confidence interval at 95% is as below
3.53 ≤ meandelivery time ≤ 4.47
In the 95% confidence interval it has been seen that the average delivery time is lies
between 3.53 and 4.47 which is larger than the 3 days. But according to the manager the
delivery time does not exceed 3 days. Therefore the claim of the manager is not true. Hence
the claim is rejected.
Part (d)
Test statistic = 4.17
P-value= 0.0002

4APPLIED MANAGEMENT STATISTICS
Alpha = 0.05
From the test it is clear that P-value < alpha (alpha=0.05). Hence the null hypothesis
is significant. Therefore it may be concluded at 5% significance level that the delivery time of
the product is exceed 3 days.
Answer to the question 3
Part (a)
The number of kids (n) = 100
The mean of the study = 25
Standard deviation = 5
The 99% confidence interval of the mean of kinds is
Mean ±2.58 * (standard deviation / sqrt (n))
= 25±2.58 *(5/ sqrt (100))
= 25±2.58 * 0.5
= (23.71, 26.29)
23.71 ≤ meanof kinds∈ Barcelona at age (6−11)≤ 26.29
Part (b)
At 99% confidence interval the mean of all kids which age 6-11 is lies between 23.71
and 26.29. It is given that the mean watching time is 25. Therefore it is clear that the 99%
confidence lies within the mean time. Hence at 99% confidence interval the mean of all kids
which age 6-11 may not be rejected.

5APPLIED MANAGEMENT STATISTICS
Answer to the question 4
Regression Output
Part (a)
The independent variable of the study is work experience and the dependent variable
is annual income. From the regression output it is clear that the correlation between the work
experience and annual income is 0.93. It means that the relationship between the annual
income and work experiences is positive and strong because which is close to the 1.
Part (b)
The R-square that is the coefficient of determination is 0.86. This indicate that the
relationship between the annual income and work experiences is 86%, which is strong and
positive.
Part (c)
The regression model or equation is defined as below
Annual income = 17351+1362 * work experiences

6APPLIED MANAGEMENT STATISTICS
The slope of the regression model is 17351 and the coefficient of the independent
variable is 1362.
Part (d)
Given that
Work experience = 15 years
Thus
Annual income = 17351+1362 * work experiences
= 17351+ (1362 * 15)
= 37781
Hence the average annual income of a person at 15 years experiences is 37781.
Answer to the question 5
It is given that the total number of observations is 293. Therefore there is a 3 digit
numbers has to be generate. The first sample observations on the list would like 001 and the
last would be 293.
Now there are some samples with 3 digit numbers are given below and which starts
with first row from the table. The samples are
492, 808, 892,435, 779, 002, 838, 116, 307, 275, 898,630, 234,861, 870, 416, 570,
746, 808, 612,980, 839,734, 920,775, 450,914, 389, 865, 923, 250, 788, 612, 978,
496, 976, 539, 155, 008, 078, 629, 939, 123, 0.45, 484, 598, 560,952, 066, 412.
In the selection of 3 digit numbers there are some conditions has been applied.

7APPLIED MANAGEMENT STATISTICS
The first condition is reject the numbers which is larger than 293. The second
condition is the numbers which is lesser than 293 but repeated among them a single one
number has been selected for the sample.
Therefore the 10 sample observations are
002,116, 275, 234, 250, 155,008, 078, 123, 045.
Hence the selected mobile phones are iPhone 7 plus, LG G4, Sony Xperia XA1 ultra,
HTC Desire 300, HTC Desire C, LG G3 Beat, Apple iPhone 8, Samsung Galaxy Note 2, LG
Nexus 5X, Samsung Galaxy S7.

8APPLIED MANAGEMENT STATISTICS
Bibliography
De Winter, J.C., 2013. Using the Student's t-test with extremely small sample sizes. Practical
Assessment, Research, and Evaluation, 18(1), p.10.
Giometto, A., Formentin, M., Rinaldo, A., Cohen, J.E. and Maritan, A., 2015. Sample and
population exponents of generalized Taylor’s law. Proceedings of the National Academy of
Sciences, 112(25), pp.7755-7760.
Lee, D.K., 2016. Alternatives to P value: confidence interval and effect size. Korean journal
of anesthesiology, 69(6), p.555.
Morey, R.D., Hoekstra, R., Rouder, J.N., Lee, M.D. and Wagenmakers, E.J., 2016. The
fallacy of placing confidence in confidence intervals. Psychonomic bulletin & review, 23(1),
pp.103-123.
Pataky, T.C., Vanrenterghem, J. and Robinson, M.A., 2015. Zero-vs. one-dimensional,
parametric vs. non-parametric, and confidence interval vs. hypothesis testing procedures in
one-dimensional biomechanical trajectory analysis. Journal of biomechanics, 48(7), pp.1277-
1285.
Pencina, M.J., Navar-Boggan, A.M., D'Agostino Sr, R.B., Williams, K., Neely, B.,
Sniderman, A.D. and Peterson, E.D., 2014. Application of new cholesterol guidelines to a
population-based sample. N Engl J Med, 370, pp.1422-1431.
Sivakumar, T. and Venkatesan, R., 2016. A New Image Encryption Method Based on
Knight's Travel Path and True Random Number. J. Inf. Sci. Eng., 32(1), pp.133-152.

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