Statistics and Business Decision Making

This document presents a solved statistics assignment that explores the use of statistical tools in business decision making. It includes calculations of mean, median, mode, standard deviation, z-value, and confidence intervals. The assignment also discusses the relationship between hypothesis testing and confidence intervals, illustrating how they are used to evaluate population parameters and make informed business decisions.

STATICS QUESTION

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
Question 1........................................................................................................................................1
(a).................................................................................................................................................1
(b).................................................................................................................................................1
©..................................................................................................................................................1
(d).................................................................................................................................................1
Question 2........................................................................................................................................2
(a).................................................................................................................................................2
(b).................................................................................................................................................2
©..................................................................................................................................................2
........................................................................................................................................................3
(d).................................................................................................................................................3
Question 3........................................................................................................................................3
(a).................................................................................................................................................3
(b).................................................................................................................................................3
©..................................................................................................................................................3
Qustion 4..........................................................................................................................................3
(a).................................................................................................................................................3
(b).................................................................................................................................................4
©..................................................................................................................................................4
CONCLUSION................................................................................................................................4
REFERENCE..................................................................................................................................5
Table 190% CI values......................................................................................................................3

Table 2Computation of sample size................................................................................................3

1 | P a g e

INTRODUCTION
Statistics is the one of the fastest growing domain in the world as with passage of time
significence of analytics and data visualization is growing at rapid rate. These tools are assisting
managers in making strong business decisions. In the current report varied statistical tools are
applied on dataset like descriptive staitistics and confidence interval calculations etc. Meaningful
interpretation of results are also done in the present research study. At end of the report,
conclusion section is prepared in the report.
Question 1
(a)
Quiz 1 Quiz 2 Quiz 3 Quiz 4
Mean 72 Mean 72 Mean 76 Mean 76
Median 72 Median 72 Median 72 Median 86.5
Mode 60 Mode 65 Mode 72 Mode #N/A
Standard
Deviation
13.232
95549
Standard
Deviation
6.6666
66667
Standard
Deviation
11.411
49518
Standard
Deviation
27.430
72082
Skewness
1.0130
59714 Skewness
6.1679
1E-17 Skewness
1.5713
00438 Skewness
-
1.8660
2837
(b)
Quiz 1 and 2 results as well as quiz 3 and 4 results agree with each other. It can be seen
that mean value in case of first 2 quizes are 72 and for 3 and 4 quiz mean value is 76. Hence,
results of quiz to some extent agree.
©
Major strength of mean value for all quiz is that is give overview of the variable. Major
weakness is that it does not reflect how many other values apart from mean are in dataset.
Median strength is that it divide data in to two parts (Descriptive statistics, 2017). Weakness is
that it does not directly reflect trends that are in dataset. Mode value major strength is that it
indicate value that occur most of times in dataset. Limitation is that if any value is not repeating
in data then mode value remain zero.
(d)
Data is not symetric and not skewed because charts of all four quizes are not in bell shape
curve.
2 | P a g e

Question 2
(a)
Table 190% CI values
Mean 19.00
Median 0.00
Mode 0.00
Standard deviation 1.30
Z value 1.645
Square root 10
STDEV/SR 0.13
Z*STDEV/SR 0.2139
Mean-(Z*STDEV/SR) 18.79
Mean+(Z*STDEV/SR) 19.21
(b)
By only considering almong proportion normality in data can not be assumed as it cover
only 19% of data set instead of 68% in order to form normally probability distributiion.
©
Table 2Computation of sample size
CI 90%
Error 0.3
CI value 1.645
Error/CI value 0.1824
(Error/CI value)^2 0.0333
P value 0.91
1-P value 0.09
P value*1-P value 0.0819
n 2.4625
Interpretation
Sample size is 2.46 at 90% confidence interval and standard error +/- 0.3. Small sample
size is observed because condition was that deviation must be only by 0.3 points which is very
low.
(d)
Quality control manager at Planter need to understand sample because it is very
important to identify way in which sample data is disributed (The normal disribution, 2017). On
3 | P a g e

basis of information of distribution of sample data it can be identified whether by using normal
distirbution probability can be computed or any other approach need to be used to compute
probability of happening of certain event.
Question 3
(a)
It can be seen that in secon table value of P computed is 0.00<0.05 and it clearly means
that price is significently different from zero. Value of cofficient is 88.49 which means that with
change in independent variable dependent variable value changed by 88.49 points.
(b)
R square reflect percentage change that can be observed in dependent variable with
change in independent variable (Whats a good value of R squares, 2017). R square value is 0.01
and this reflect that with change in dependent variable independent variable change by 1%.
©
It can be concluded that with change in quality product price changed significently as
value of level of significence is 0.00<0.05.
Qustion 4
(a)
Mean 3.35
Median 0.00
Mode 0.00
Standard deviation 0.25
Z value 1.96
Square root 4.242640687
STDEV/SR 0.058925565
Z*STDEV/SR 0.115494108
Mean-(Z*STDEV/SR) 3.23
Mean+(Z*STDEV/
SR) 3.47
There is no significent distribution between 3.25 and 3.35 as value 3.25 comes in 90%
confidence interval which is 3.23 and 3.47.
4 | P a g e

(b)
Yes, confidence interval cover value 3.25 in the maximum and minimum limit at 95%
confidence interval where values lie in range of 3.23 to 3.47.
©
Hypothesis test and confidence interval are same. This is because whenever any
hypothesis testing is done then an attempt is made to identify whether value that is tested lie in
specific confidence interval. For example there are two variables photomasks and linewidth.
There is hypothesis under which it will be identified linewidth have mean value of 500
micrometer at different level of photomasks (Confidence intervals and hypothesis testing, 2017).
By considering standard deviation and mean value of variables applying statistical tool it is
identfied that at specific confidence interval that value comes or not. Hence, from this point of
view it can be said that confidence interval and hypothesis are related to each other. It can be
said that hypothesis is prepared in respect to population parameter and if this value does not
come in range of 90% or any level of confidence interval then in that case null hypothesis is
accepted. Thus, in this way hypothesis testing and confidence interval are coorelated to each
other. It can also be said that upon confidence interval it depend whether hypothesis will be
accepted or rejected.
CONCLUSION
On basis of above discussion it is concluded that there is significent importance of
accounts for the business firms because by using same lots of facts are identified and it is
identified that in which direction work need to be done in the business. It is the statistics by using
which all areas in which firm operating can be analyzed deeply and it can be identified that in
which areas firm is weak or strong. Thus, it can be said that there is huge importance of statistics
for business managers.
5 | P a g e

REFERENCE
Online
Confidence intervals and hypothesis testing, 2017. [Online]. Available through:<
http://davidmlane.com/hyperstat/B15183.html>.
Descriptive statistics, 2017. [Online]. Available through:<
https://medanth.wikispaces.com/Descriptive+Statistics>.
The normal disribution, 2017. [Online]. Available through:<
http://www.stat.yale.edu/Courses/1997-98/101/normal.htm>.
Whats a good value of R squares, 2017. [Online]. Available through:<
https://people.duke.edu/~rnau/rsquared.htm>.
6 | P a g e