Business Statistics Homework: Hypothesis Testing and Probability

This Business Statistics homework assignment covers several key statistical concepts. Part A focuses on descriptive statistics, including calculating mean, median, range, standard deviation, and variance from raw data presented in a table and histogram. Part B calculates a confidence interval. Part C discusses the significance of statistics for managers in business decision-making. Part D involves hypothesis testing, explaining the process and providing a calculation of probability. Finally, Part E presents a probability calculation related to salary. The assignment uses tables, histograms and statistical calculations to analyze data and draw conclusions, with references to relevant literature.

BUSINESS STATISTICS

TABLE OF CONTENTS
Part A...............................................................................................................................................1
(1)................................................................................................................................................1
(2)................................................................................................................................................2
(3)................................................................................................................................................2
Part B...............................................................................................................................................2
Part C...............................................................................................................................................3
Part D...............................................................................................................................................4
(1)................................................................................................................................................4
(2)................................................................................................................................................4
(3)................................................................................................................................................4
Part E................................................................................................................................................4
REFERENCES................................................................................................................................................6
Figure 1Histogram...........................................................................................................................1
Figure 2Histogram...........................................................................................................................3
Table 1Histogram raw data..............................................................................................................1
Table 2Descrptive statistics calculation...........................................................................................2
Table 3Calculation of CI.................................................................................................................2
Table 4Calculation of probability....................................................................................................4
Table 5Calculation of probability....................................................................................................4

Part A
(1)
Table 1Histogram raw data
Row
Labels
Count of
var
29.5-30 1
30-30.5 3
30.5-31 8
31-31.5 11
31.5-32 11
32-32.5 9
32.5-33 5
33-33.5 2
Grand
Total 50
Figure 1Histogram
1

(2)
Table 2Descrptive statistics calculation
Mean 31.56
Median 31.55
Mode 31.4
Range 3.5
STDEV 0.797701
Variance 0.893141
(3)
Normal distribution graph or histogram chart is used by the data scientists to identify
whether data is normally distributed. In many tests it is condition that data must be normally
distributed only then test may show accurate results. Example of such test are regression models.
Mean is used by the researchers to identify average performance of the variable and median is
used to classify data in to two parts from middle. Mean value in above table is 31.55 which
reflect that on an average car run 31.55 KM per ltr. Range reflect the difference between
maximum and minimum value which means it reflect extent to which values are deviating in
dataset (El-Nasr, Drachen and Canossa, 2016). Range value is 3.5 which reflect that value is not
deviating at fast pace. Standard deviation and variance both also reflect deviation in data points
from mean value. If standard deviation is high then in that case it can be said that variable is
highly volatile in nature. Standard deviation value is only 0.79 which is very low and reflect that
value of data set is not deviating at fast pace.
Part B
Table 3Calculation of CI
Mean 11.09
STDEV 14.4
Sample size 30
DF 29
2

Confidence level 95%
Alpha 0.025
Look at alpha and DF value in t table 2.04523
STDEV/SQRT (Sample size) 2.629068
T table value* (STDEV/SQRT (Sample
size)) 5.377049
Lower level 5.712951
Upper level 16.46705
Figure 2Histogram
Part C
Leaning of statistics is very helpful for the managers. This is because in the business overall
performance of the company is affected by the multiple factors (Gandomi and Haider, 2015). It
is the statistics by using which one can find out that which of factor play crucial role in
generating profit or loss in the business. On basis of results of regression manager can receive
input or direction where work must be done to improve performance. Thus, it can be said that
there is huge significance of statistics for the managers.
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Part D
(1)
Hypothesis test is the process under which relationship between two or more variables is
identified. It assists analyst in identifying extent to which two variables are related to each other
(Najafabadi and et.al., 2015).
(2)
Steps vary from one tool to another, if one does calculation manually then formula for each
approach are also different (Tsai and et.al., 2015). But usually first of data is discussed between
analysts and relation between them is identified. On basis of type of variable and research
objective specific tool is used to analyse data.
(3)
Table 4Calculation of probability
Sample mean 112
Population mean 100
Standard deviation 15
Z 4.38178
Probability 0.99
There is 99% chances that sample mean will be greater then population mean. Hence, professor
claims right.
Part E
Table 5Calculation of probability
Sample mean 43260
Population mean 42000
Standard deviation 5230
Z 1.319561
Probability 0.9
There are 90% chances that assistant professor earned more than $42000 per year.
4

5

REFERENCES
Books and Journals
El-Nasr, M.S., Drachen, A. and Canossa, A., 2016. Game analytics. Springer London Limited.
Gandomi, A. and Haider, M., 2015. Beyond the hype: Big data concepts, methods, and
analytics. International journal of information management. 35(2). pp.137-144.
Najafabadi, M.M. and et.al., 2015. Deep learning applications and challenges in big data
analytics. Journal of Big Data. 2(1). p.1.
Tsai, C.W. and et.al., 2015. Big data analytics: a survey. Journal of Big data. 2(1). p.21.
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