Business Statistics Solved Assignment

This document presents a comprehensive collection of solved assignments for a Business Statistics course. It covers various statistical methods, including descriptive statistics, regression analysis, ANOVA, and hypothesis testing. The solutions are detailed and include interpretations of the results, along with relevant charts and tables. The topics covered encompass analyzing film revenue, student salaries, house prices, and mobile phone ratings. Each section presents data analysis, interpretation of statistical outputs (like R-squared, p-values, confidence intervals), and conclusions drawn from the analysis. The appendix contains numerous tables and figures supporting the analyses performed throughout the document.

BUSINESS STATISTICS

TABLE OF CONTENTS
BUSINESS STATISTICSTABLE OF CONTENTS......................................................................1
Friday...............................................................................................................................................7
(A)................................................................................................................................................7
(b).................................................................................................................................................9
©................................................................................................................................................10
(d)...............................................................................................................................................10
(e) 90% confidence interval for the population mean film rating.............................................10
(g)...............................................................................................................................................11
(h)...............................................................................................................................................11
(I)...............................................................................................................................................11
(J)...............................................................................................................................................11
(K)..............................................................................................................................................11
(N)..............................................................................................................................................12
(O)..............................................................................................................................................12
Monday..........................................................................................................................................13
.......................................................................................................................................................14
.......................................................................................................................................................14
(B)..............................................................................................................................................14
©................................................................................................................................................15
(D)..............................................................................................................................................16
(E)..............................................................................................................................................16
(F)..............................................................................................................................................16
(g)...............................................................................................................................................16
(H)..............................................................................................................................................16
(I)...............................................................................................................................................16
(J)...............................................................................................................................................16
(K)..............................................................................................................................................17
(L)..............................................................................................................................................17
(M).............................................................................................................................................17
(o)...............................................................................................................................................18

Thursday........................................................................................................................................19
(A)..............................................................................................................................................19
(B)..............................................................................................................................................21
©................................................................................................................................................22
(D)..............................................................................................................................................22
(E)..............................................................................................................................................22
(F)..............................................................................................................................................22
(G)..............................................................................................................................................23
(H)..............................................................................................................................................23
(I)...............................................................................................................................................23
(J)...............................................................................................................................................23
(K)..............................................................................................................................................23
(L)..............................................................................................................................................23
(M).............................................................................................................................................24
(O)..............................................................................................................................................24
Tuesday..........................................................................................................................................25
(A)..............................................................................................................................................25
©................................................................................................................................................27
(D)..............................................................................................................................................28
(E)..............................................................................................................................................28
(F)..............................................................................................................................................28
(G)..............................................................................................................................................28
(H)..............................................................................................................................................28
(I)...............................................................................................................................................28
(J)...............................................................................................................................................28
(K)..............................................................................................................................................28
(L)..............................................................................................................................................29
(M).............................................................................................................................................29
(O)..............................................................................................................................................29
Wednesday.....................................................................................................................................30
(A)..............................................................................................................................................30

(B)..............................................................................................................................................32
©................................................................................................................................................33
.......................................................................................................................................................33
(D)..............................................................................................................................................33
(E)..............................................................................................................................................33
(F)..............................................................................................................................................33
(G)..............................................................................................................................................33
(H)..............................................................................................................................................33
(I)...............................................................................................................................................34
(J)...............................................................................................................................................34
(K)..............................................................................................................................................34
(L)..............................................................................................................................................34
(M).............................................................................................................................................34
(O)..............................................................................................................................................34
APPENDIX....................................................................................................................................35
Table 1: Contingency table............................................................................................................34
Table 2: Calculation of R and R square.........................................................................................34
Table 3: Calculation of ANNOVA................................................................................................35
Table 4: P value table....................................................................................................................35
Table 5: Calculation of confidence interval...................................................................................35
Table 6: Regression statistics.........................................................................................................35
Table 7: ANNOVA........................................................................................................................36
Table 8: Calculation of t-stat.........................................................................................................36
Table 9: Calculation of R and R square.........................................................................................36
Table 10: Level of significance.....................................................................................................36
Table 11: Slope coefficient estimates............................................................................................37
Table 12: Prediction by using regression equation when review of movie is 30..........................37
Table 13: Predicted value of revenue on the basis of equation when movie is released on 4000
theaters...........................................................................................................................................37
Table 14 Descriptive statistics.......................................................................................................42

Table 15 Contingency table...........................................................................................................42
Table 16 Table of regression.........................................................................................................43
Table 17 Table of ANNOVA........................................................................................................43
Table 18 Table of coefficients.......................................................................................................43
Table 19 Range of bedrooms at 99% confidence interval.............................................................44
Table 20 Computation of regression statistics...............................................................................44
Table 21Calculation of ANNOVA................................................................................................44
Table 22 Coefficients of variables.................................................................................................44
Table 23 Statistics of regression for G part of Thursday...............................................................45
Table 24 Table of ANNOVA........................................................................................................45
Table 25 Computation of coefficients...........................................................................................45
Table 26 Contingency table...........................................................................................................47
Table 27 Calculation of regression................................................................................................47
Table 28 Computation of ANNOVA.............................................................................................47
Table 29 Calculation of coefficient...............................................................................................48
Table 30 Range at 90% confidence interval..................................................................................48
Table 31 Summary statistics of one way ANNOVA.....................................................................48
Table 32 Variation between and within groups.............................................................................48
Table 33 Regression statistics........................................................................................................49
Table 34 ANNOVA table..............................................................................................................49
Table 35 Coefficient table.............................................................................................................49
Table 36 Table of regression.........................................................................................................50
Table 37ANNOVA table...............................................................................................................50
Table 38 Calculation of coefficient...............................................................................................50
Table 39 95% Confidence interval................................................................................................50
Table 40 One way ANNOVA........................................................................................................51
Table 41Calculation of regression.................................................................................................51
Table 42 Computation of ANNOVA.............................................................................................52
Table 43 Coefficient table..........................................................................................................................52
Figure 1: Shape of Theater..............................................................................................................9

Figure 2: Shape of Metacritic..........................................................................................................9
Figure 3: Shape of gross................................................................................................................10
Figure 4: Number of theater..........................................................................................................10
Figure 5: Box and Whisker plot.....................................................................................................11
Figure 6 Chart on salary................................................................................................................14
Figure 7 Chart on satisfaction........................................................................................................15
Figure 8 Chart on ATAR...............................................................................................................15
Figure 9Chart on Satisfaction........................................................................................................16
Figure 10 Box and Whisker chart..................................................................................................16
Figure 11 Regression equation......................................................................................................18
Figure 12Chart on number of bedrooms........................................................................................20
Figure 13Chart on price of homes.................................................................................................21
Figure 14 Chart on land area.........................................................................................................21
Figure 15 Chart on mile distance...................................................................................................22
Figure 16 Distance graph...............................................................................................................22
Figure 17 Box and Whisker chart..................................................................................................23
Figure 18 Chart on battery score...................................................................................................26
Figure 19 Chart on pic density.......................................................................................................27
Figure 20 Chart on score................................................................................................................27
Figure 21 Chart on review score....................................................................................................28
Figure 22 Box and whisker chart...................................................................................................28
Figure 23Regression equation.......................................................................................................30
Figure 24 Price of cars...................................................................................................................31
Figure 25 Power capacity of car....................................................................................................32
Figure 26 Weight of cars...............................................................................................................32
Figure 27 Fuel efficiency of car.....................................................................................................33
Figure 28 Distribution of fuel........................................................................................................33
Figure 29Box and Whisker plot.....................................................................................................34
Figure 30 Regression equation......................................................................................................35
Figure 31Contingency table...........................................................................................................40
Figure 32 Regression table............................................................................................................40

Figure 33 ANNOVA table.............................................................................................................40
Figure 34 Coefficient table............................................................................................................41
Figure 35 95% Confidence interval...............................................................................................41
Figure 36 Statistics of regression...................................................................................................41
Figure 37ANNOVA table..............................................................................................................42
Figure 38 Table of coefficients......................................................................................................42

Friday
(A)
Gross
revenue Theatres Metacritic Sequel/Reboot Action
Mean 65.93 2460.05 54.71 0.19 0.18
Median 26.82 2720.00 56.00 0.00 0.00
Mode #N/A 3003 81 0 0
Standard deviation 111.866 1033.737278 17.98380642 0.39865 0.38822
Interpretation
 Gross- Mean value of gross revenue is 65.93 and value of median is 26.82. It means that on
average basis, revenue of 65.93 million USD is earned by the business firms. Moreover,
26.82 million USD is the medium value of total amount of revenue earned by business
firms. There is no value of the revenue that is repeating multiple times in data set. Hence,
value of mode is NA. Standard deviation is equivalent to 111.866 which means that by
higher amount, revenue of different movies deviate from mean value.
 Theatres- From the above table, it can be observed that value of mode is 3003. This means
that most of the movies are released in 3003 theaters. Mean value is 2460 and it is reflecting
that on average basis, films are screened on mentioned number of theaters. Standard
deviation value is quite high which indicates that there is huge difference among the movies
in terms of their release on specific number of theater screens.
 Metacritic- On an average, films are receiving rating of 54.71 from views. Statistics indicate
that most often, viewers give a rating of 81 to most of the movies that are in data set. Value
of standard deviation is very low which means that maximum movies get similar ratings
from viewers.
 Sequel/Reboot- There are very small values of mean and standard deviation. Value of
median and mode is zero. This reflects that sequel parts of most of the movies are not
prepared.
 Action- Trends that were observed in the sequel are again repeating in the action. Hence, it
can be said that less action movies are screened in theaters of USA.

Figure 1: Shape of Theater
Figure 2: Shape of Metacritic

Figure 3: Shape of gross
(b)
Figure 4: Number of theater
From the above image, it can be observed clearly that data related to number of theaters in
which movies are released is not normally distributed. This is evident from the fact that line goes
straight in upward direction. Its shape is not similar to the bell curve.

©
Figure 5: Box and Whisker plot
Box and Whisker plot clearly revealed that there are no outliers in the data. If there will be
outlier then length of whisker will be three times greater than the size of relevant box.
(d)
Interpretation
Value of level of significance is 0.10>0.05 which means that there is not a big difference
between dependent and independent variable. Gross revenue is independent of Metacritic when
the value is below 50. Values of R and R square mentioned interpretation as their values are very
low.
(e) 90% confidence interval for the population mean film rating
Interpretation
Minimum level of confidence interval is at 51.34 and maximum level at 90% confidence
interval is 58.09. This means that reviews of most of the films will lie in range of 51.34-58.09.
(f)
Interpretation
In the present case, value of level of significance is 0.393>0.05 which indicates that there
is no statistically large difference between action movies and earning of revenue above 100

million USD. Hence, if movie is not an action film then also, it can earn revenue of more than
100 million USD.
(g)
Interpretation
Level of significance is 2.97 which is above alpha value 0.05 that means the big variation
is not observed in revenue due to change in review and theaters.
(h)
Interpretation
At 5% level of significance coefficient estimate of theater are not significantly different.
As it can be seen that coefficient value is 0.05, it means that if movie is shown in another theater
by 0.05, earned revenue will get changed.
(I)
Interpretation
It can be seen that due to change in most of the variables, any big variation does not come
in revenue as value of coefficient of all variables is very low. It must be noted that coefficient
values are not interpreted in percentage form. If movie related to action then by 84.99 points,
revenue can be changed. Hence, it can be said that none of these factors put a strong influence on
revenue. This happened because people go in theater for entertainment purpose as they already
view trailer of movies and on that basis they make decisions in respect to watching a movie in
cinema hall . On that basis, they take decision with respect to watch a movie in theater. Hence,
theater, action and reviews does not affect revenue.
(J)
Adjusted R square value is reflecting that due to change in independent variable, 54%
change will come in the gross revenue. There is not a big difference between value of adjusted R
square and r square. This happened because addition of new predictor does not bring any big
change in results that were earlier produced by model.
(K)
Entire model is not statistically significant different at 5% level of significance and there is
not a big difference between gross and independent variables.