The last part of the analysis will examine the relationship between MPG and other variables in the data set and also look into the extent to which MPG can be predicted using the other variables.

1
INTRODUCTION
Statistics is one of the tools used to make decisions. This is a project in which particular
decisions regarding the data set provided are made. In this project, a sample of 93 cars
categorized into compact, small, midsize, large, sporty and van cars will be analyzed so as to find
out what the data means pertaining to the categories.
The first part of the analysis is aimed at showing how car price (for basic and top
specification models) differs by type of car and how MPG (miles per gallon) differs by type
of car.
The use of descriptive statistics is an essential tool to work with in which different measures of
dispersion are used where applicable. The use of confidence intervals, hypothesis testing and
Chi-squared are significant to explain what the data means in the context of the population since
the discussion is a bit pointless unless it is used to talk about population difference in price and
mpg.
The last part of the analysis will examine the relationship between MPG and other
variables in the data set and also look into the extent to which MPG can be predicted using
the other variables.
To find the linear relationship between mpg and other variables in the data set scatter diagrams
are used together with the application of the concepts of correlation and bivariate regression in
which tools such as coefficient of correlation and coefficient of determination apply. Equation
lines are then used to predict the mpg from variables used in each case.

2
Part 1 aim: Comparing price and mpg across categories of
vehicles
Table 1: Descriptive statistics across vehicle categories using
basic price
Compact
(‘000)
Small
(‘000)
Midsize
(‘000)
Large
(‘000)
Sporty
(‘000)
Van
(‘000)
Mean 15.69375 8.428571 24.11364 22.93636 16.85714 16.2
Median 14.05 8.2 23.05 19.9 13.7 16.6
Skewness 1.05217 1.595839 0.686664 1.14479 1.538621 0.513254
Standard Deviation 5.873156 1.493031 10.15233 6.260714 7.895346 2.02793
Coefficient of variation
(%) 37.42353 17.71393 42.10203 27.29602 46.8368 12.51809
Standard Error 1.468289 0.325806 2.164484 1.887676 2.11012 0.675977
Range 20.5 6.2 33 16.9 25.5 5.9
Minimum 8.5 6.7 12.4 17.5 9.1 13.6
Maximum 29 12.9 45.4 34.4 34.6 19.5
Sum 251.1 177 530.5 252.3 236 145.8
Count 16 21 22 11 14 9
Interpretation of descriptive statistics
Mean
Table 1 shows the basic price means of compact, small, midsize, large, sporty and van cars
respectively as $15693.75, $8428.57, $24113.64, $22936.36, $16857.14 and $16200.00 to 2
decimal places. The midsize cars category has the highest mean basic price. This may be due to
it having more new than old models and because they are highly priced. The small cars category
has the lowest mean basic price. This may result from it having more old than new models and
being low priced.

3
Median
Table 1 continues to show that the basic price medians of compact, small, midsize, large, sporty
and van cars respectively are $14050.00, $8200.00, $23050.00, $19900.00, $13700.00 and
$16600.00 to 2 decimal places. As in the mean basic price, the median basic price for midsize
cars is the highest and this is reasonable because if midsize cars are highly priced then, the
median basic price has to be high as well. If small cars are low priced, then they would have the
lowest median basic price shown in table 1.
Skewness
From table 1 the values for compact, small, midsize, large, sporty and van cars respectively in
terms of skewness are 1.05, 1.60, 0.69, 1.14, 1.54 and 0.51 to 2 decimal places. All values of
skewness are positively skewed since few prices are extremely high. The compact, small, large
and sporty have moderate positive skewness whereas the skewness for midsize and van cars is
near symmetrical.
Coefficient of variation (CV)
Standard deviation will only be used if means across variables being compared are the same, so
in this case coefficient of variation is usedto compare basic prices across car types within the
data set provided. Within table 1 the values in percentages for coefficient of variation for
compact, small, midsize, large, sporty and van cars respectively are 37.42, 17.71, 42.10, 27.30,
46.84 and 12.52 to 2 decimal places. Prices across vehicle categories are relatively nearer to their
respective means. The CV for compact, midsize and sporty cars are almost close to each other
because they have similar features.
Range
The range of basic prices of compact, small, midsize, large, sporty and van categories of cars
respectively are $20500, $6200, $33000, $16900, $25500 and $5900. The midsize category has
the highest range of car prices.

4
Table 2: Descriptive statistics across vehicle categories using top price
Compact
(‘000)
Small
(‘000)
Midsize
(‘000)
Large
(‘000)
Sporty
(‘000)
Van
(‘000)
Mean 20.725 11.90476 30.31364 25.67273 21.95714 22.03333
Median 18.5 11.3 27.35 21.9 21.2 21.7
Skewness 0.949588 0.918155 1.816957 0.912413 1.029276 0.124539
Standard deviation 7.960946 2.80329 15.08554 6.668746 8.57309 3.009152
Coefficient of variation
(%) 38.41229 23.5477 49.76487 25.976 39.04469 13.65727
Standard Error 1.143805 0.918155 1.816957 0.912413 1.029276 0.124539
Range 25.7 10.9 65.1 19.4 30.5 8.6
Minimum 11.4 7.9 14.9 18.4 11 18
Maximum 37.1 18.8 80 37.8 41.5 26.6
Sum 331.6 250 666.9 282.4 307.4 198.3
Count 16 21 22 11 14 9
Mean
According to table 2 the top price means of compact, small, midsize, large, sporty and van cars
respectively are $20725, $11904.76, $30313.64, $25672.73, $21957.14 and $22033.33 to 2
decimal places. The midsize cars category has the highest mean basic price. This may be due to
it having more new than old models and because they are highly priced. The small cars category
has the lowest mean basic price. This may result from it having more old than new models and
being low priced.
Median
The top price medians displayed in table 2 for compact, small, midsize, large, sporty and van
cars are $18500.00, $11300.00, $27350.00, $21900.00, $21200.00, $21700.00 respectively to 2
decimal places. As in the top price means in table 2, midsize category has the highest median and

5
this may also be as a result of them being highly priced. The small cars category has the lowest
median, resulting from them being low priced.
Skewness
From table 2, the values for compact, small, midsize, large, sporty and van cars in terms of
skewness are 0.95, 0.92, 1.12, 0.91, 1.03, and 0.12 respectively to 2 decimal places. These values
show positive skewness because there are few prices which are extremely high. Midsize and
sporty cars are have moderate positive skewness while the skewness for compact, small, large
and van cars are near symmetrical.
As in the basic price table 1, standard deviation will only be used if means across variables being
compared are the same, therefore coefficient of variation is used to compare top prices across
cars types within the data set provided. The values for CV in percentages in table2 for compact,
small, midsize, large, sporty and van cars are 38.41, 23.55, 49.76, 25.98, 39.04, and 13.66
respectively to 2 decimal places. Prices across vehicle categories are relatively closer to their
respective means.
Range
The range for compact small, midsize, large, sporty and van categories are $25700, $10900,
$65100 $19400, $31500 and $8600 respectively according to table 2. The van car type has the
least range resulting from having the highest and lowest price being close to each other within its
category. The midsize car type has the highest range and this is to having one very highly priced
car and one very low priced car within its category.

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Table 3: Descriptive statistics across vehicle categories using town mpg
Compact
(miles)
Small
(miles)
Midsize
(miles)
Large
(miles)
Sporty
(miles)
Van
(miles)
Mean 22.6875 29.8571 19.54545 18.3636 21.7857 17
Median 23 29 19 19 22.5 17
Skewness -0.00578 1.28788 0.038136 -0.5460 0.47679 -1.049
Standard
Error 0.480613 1.33324 0.404130 0.4527 1.04397 0.4082
Stdev 1.922455 6.1097 1.895540 1.5015 3.90617 1.2247
CV (%) 8.474 20.463 9.698 8.177 17.93 7.204
Range 6 24 7 4 13 3
Minimum 20 22 16 16 17 15
Maximum 26 46 23 20 30 18
Sum 363 627 430 202 305 153
Count 16 21 22 11 14 9
Mean
Table 3 shows that the town mpg means for compact, small, midsize, large, sporty and van
categories of cars respectively are 22.69miles, 29.86miles, 19.55miles, 18.36miles, 21.79miles
and 17.00miles to 2 decimal places.
This table indicates that small cars travel more miles having consumed a gallon and with this one
can come to the conclusion that small cars are the most efficient and consume less fuel as
compared to other categories. This is because they have small engine sizes and small weight as
compared to other categories and also that they may be owned by town drivers. On the other
hand van cars travel less miles in consumption of 1 gallon as compared to other categories
meaning they consume a lot of fuel and are not efficient. The general rule is that efficient cars
consume less fuel.
Median
Table 3 continues to show that the town mpg medians of compact, small, midsize, large, sporty
and van cars respectively are 23miles, 29miles, 19miles, 19miles, 22.5miles and 17miles.
According to the table medians of midsize and large cars are the same this implies at some point
these categories travel the same distance having consumed a gallon. Small cars are the most
efficient as compared to other categories since they have the highest median town mpg.

7
Skewness
terms of skewness are -0.01, 1.29, 0.04, -0.55, 0.48 and -1.05 to 2 decimal places.
Compact, large and van categories have negative skewness while small, midsize and sporty have
positive skewness.
Within table 3 the values in percentages for coefficient of variation for compact, small, midsize,
large, sporty and van cars respectively are 8.47, 20.46, 9.70, 8.18, 17.93 and 7.20 to 2 decimal
places. Compact, midsize, large and van cars’ have a more relatively small deviation from their
town mpg means and this is because they almost have similar characteristics for instance they
have engine sizes which are almost the same taking an Audi 90 with 2.8l engine size from the
compact category and a Dodge Dynasty with 2.5l engine size we can see they are not that
different. As for small and sporty categories they have a relatively small deviation from their
town mpg means as they have similar characteristics as well.
Range
The range of town mpg of compact, small, midsize, large, sporty and van categories of cars
respectively are 6miles, 24miles, 7miles, 4miles, 13miles and 3miles. The small category has the
highest range of miles travelled in a gallon since the largest number of miles travelled as
compared to other variables hence more dispersion in miles per gallon travelled.

8
Table 4: Descriptive statistics across vehicle categories using best mpg
Compact
(miles)
Small
(miles)
Midsize
(miles)
Large
(miles)
Sporty
(miles)
Van
(miles)
Mean 29.875 35.47619 26.72727 26.72727 28.78571 21.8888
Median 30 33 26.5 26 28.5 22
Skewness 0.589052 1.184606 0.121628 -0.09127 0.501811 -0.07115
Standard Error 0.735272 1.224004 0.535258 0.383546 0.973148 0.48432
Standard Deviation 2.941088 5.609091 2.510584 1.272078 3.641187 1.45296
Coefficient of
variation (%) 9.844647 15.81086 9.39334 4.759475 12.64928 6.63791
Range 10 21 9 3 12 4
Minimum 26 29 22 25 24 20
Maximum 36 50 31 28 36 24
Sum 478 745 588 294 403 197
Count 16 21 22 11 14 9
Mean
Table 4 shows the best miles per gallon means of compact, small, midsize, large, sporty and van
cars respectively as 29.88miles, 35.48miles, 26.73miles, 26.73miles, 28.79miles and
21.89milesto 2 decimal places. This denotes that of all the various car types, small cars have the
highest average miles per gallon consumption figure. This is to say that across a long distance of
miles they consume the least fuel. This may rightfully be influenced greatly by the fact that they
are small cars i.e. with a small body, generally small compartments. This may also be spurred on
by the fact that small cars have a relatively low engine size in comparison with the other car
types.It is also visible that vans have the lowest mean fuel consumption. This suggests that
across all the vehicle types vans are the most efficient in relation to low fuel consumption.The
table also brings to light the fact that midsize and large cars consume the same average (mean)
miles per gallon.
Median
Table 4 continues to show that the town mpg medians of compact, small, midsize, large, sporty
and van cars respectively are 30miles, 33miles, 26.5miles, 26miles, 28.5miles and 22miles.
According to the table medians of midsize and large cars are almost the same,this implies at

9
some point these categories travel the same distance having consumed a gallon. Small cars are
the most efficient as compared to other categories since they have the highest median town mpg.
Skewness
terms of skewness are 0.59, 1.18, 0.12, -0.09, 0.50and -0.07 to 2 decimal places.
Compact, small, midsize and sporty categories have positiveskewness while large and van
categories have positive skewness.
Within table 4 the values in percentages for coefficient of variation for compact, small, midsize,
large, sporty and van cars respectively are 9.84, 15.81, 9.39, 4.76, 12.65 and 6.64 to 2 decimal
places. All categories are not relatively far away from their respective means.
Range
The range of town mpg of compact, small, midsize, large, sporty and van categories of cars
respectively are 10miles, 21miles, 9miles, 3miles, 12miles and 4miles. The small category has
the highest range of miles travelled in a gallon since the largest number of miles travelled as
compared to other variables hence more dispersion in miles per gallon travelled.

10
Hypothesis testing
This is to test if the population means are the same where there are interesting differences (where
means are almost the same). A t-test will be used in each case since n (being the number of
vehicles per car category) is less than 30 (it is small).
Basic price
Sporty and van categories
At 1% significance level the null hypothesis is not rejected since there is sufficient evidence that
the population means are equal and at 5% significance level the null hypothesis is not rejected as
well. This implies that the basic prices of both sporty and van categories are close to each other.
Midsize and large categories
At 1% significance level the null hypothesis is not rejected since there is adequate evidence that
the population means are equal and at 5% significance level the null hypothesis is also not
rejected, implying that basic prices of midsize and large categories are close to each other.
Top price
Compact and sporty categories
At 1% significance level the null hypothesis is not rejected as there is sufficient evidence that the
population means are equal and at 5% significance level the null hypothesis is not rejected. This
implies that top prices of compact and sporty categories are not so different.
Sporty and van categories
At both 1% and 5% significance levels the null hypotheses is not rejected as there is sufficient
evidence that the population means are equal.This implies that top prices of sporty and van
categories are not so different.

11
Mpg town
At both 1% and 5% significance levels the null hypotheses are not rejected as there is sufficient
evidence that the population means are equal. This implies that midsize and large cars travel
almost the same distance per gallon.
At both 1% and 5% significance levels the null hypotheses are not accepted as the population
means are not equal. The implication here is that compact and sporty cars travel very different
distances per gallon.
Mpg best
evidence that the population means are equal.This implies that compact and sporty cars travel
evidence that the population means are equal.This implies that midsize and large cars travel

12
Confidence intervals
To infer on population means using sample means, confidence intervals are used since there is no
information given about the population. The discussion is pointless unless it is used to talk about
the population. The 99% confidence level is used for more confidence. These intervals are
calculated using the formula in appendix 6.
Compact
 The 99% confidence interval for the true population basic price meanfor compact cars is
between $11367.12 and $20020.38.
 The 99% confidence intervalfor the true population top price meanfor compact cars is
between $6040.10 and $17769.42.
 The 99% confidence interval for the true population town mpg mean for compact cars is
between 21.27miles and 24.10miles.
 The 99% confidence interval for the true population best mpg mean for compact cars is
between 27.71miles 32.04miles.
Small
 The 99% confidence interval for the true population basic price mean for small cars is
between $7501.54 and $9355.60.
 The 99% confidence interval for the true population top price mean for small carsis
between $10628.72 and $13180.81.
 The 99% confidence interval for the true population town mpg mean for small cars is
between 26.06milesand 33.65miles.
 The 99% confidence interval for the true population best mpg mean for small cars is
between 31.99miles and 38.96miles
Midsize
 The 99% confidence interval for the true population basic price mean for midsize cars is
between $17985.21 and $30242.07.
 The 99% confidence intervalfor the true population top price mean for midsize cars is
between $21207.28 and $39419.10.

13
 The 99% confidence interval for the true population town mpg meanfor midsize cars is
 The 99% confidence interval for the true population best mpg meanfor midsize cars is
Large
 The 99% confidence interval for the true population basic price meanfor large cars is
between $16953.80 and $28918.92.
 The 99% confidence intervalfor the true population top price mean for large cars is
between $19300.26 and $32045.19.
 The 99% confidence interval for the true population town mpg meanfor large cars is
 The 99% confidence interval for the true population best mpg meanfor large cars is
Sporty
 The 99% confidence interval for the true population basic price meanfor sporty cars is
between $10500.88 and $23213.40.
 The 99% confidence intervalfor the true population top price mean for sporty cars is
between $15055.24 and $28859.04.
 The 99% confidence interval for the true population town mpg meanfor sporty cars is
 The 99% confidence interval for the true population best mpg meanfor sporty cars is
between 25.85miles and 31.71miles
Van
 The 99% confidence interval for the true population basic price meanfor van cars is
between $13931.84 and $18468.16.
 The 99% confidence intervalfor the true population top price mean for van cars is
between $18667.71 and $25398.96.
 The 99% confidence interval for the true population town mpg meanfor van cars is
 The 99% confidence interval for the true population best mpg meanfor van cars is

14
Probability
Basic price
The general is any car falling below the overall basic mean price ($17126) found in appendix 7is
cheap and any car falling above this price is expensive.
Table 5:93 cars classified each in relation to the overall basic meanpricebeing either lower
(cheap), higher (expensive) according carcategory.
Category Low (cheap) High (expensive) Total
Compact 11 5 16
Small 21 0 21
Midsize 9 13 22
Large 0 11 11
Sporty 10 4 14
Van 7 2 9
Total 58 35 93
The probability that a car would:
1. be compact and expensive is:
= (35/93)*(5/35)
= 5/93
2. come from the small category is:
= 21/93
3. be midsize and cheap is:
= (58/93)*(9/58)
= 3/31
4. be large, given it is expensive is:
=11/11
= 1
5. be cheap, given it is sporty is:
= 10/58
= 5/29
6. come from the van category is:
=3/31

15
Top price
Any car falling below the overall top mean price ($21899) found appendix 7 is considered cheap
and any car falling above this overall top mean price is considered expensive.
Table 6: 93 cars classified each in relation to the overall top mean pricebeing either lower
(cheap), higher (expensive) according carcategory.
Category Low (cheap) High (expensive) Total
Compact 10 6 16
Small 21 0 21
Midsize 8 14 22
Large 5 5 11
Sporty 8 6 14
Van 5 4 9
Total 57 35 93
1. be compact and expensive is:
= (35/93)*(6/35)
= 2/31
2. come from the small category is:
= 21/93
3. be midsize and cheap is:
= (58/93)*(8/58)
= 8/93
4. be large, given it is expensive is:
= 5/11
5. be cheap, given it is sporty is:
= 8/57
6. come from the van category is:
=3/31
Considering table 5,6 and the above calculations, it would be fair to say that midsize cars are the
most expensive on average since most prices cars within the category are above the overall mean
basic price and overall mean top price as compared to the other types. On the other hand, it

16
would also be reasonable to say that small cars are the cheapest as compared to other types since
most car prices fall below the overall mean basic price and the overall mean top price.
Mpg town
Any car falling below the overall town mpg mean (22.37miles) found in appendix 7 is
considered non-efficient and any car falling above this overall town mpg mean is considered
efficient.
Table 7:93 cars classified each in relation to the overall town mpgbeing either non-efficient
or efficientaccording carcategory.
Category Non- efficient Efficient Total
Compact 7 9 16
Small 14 7 21
Midsize 12 10 22
Large 5 6 11
Sporty 6 8 14
Van 2 7 9
Total 46 47 93
1. be compact and efficient is:
= (47/93)*(9/47)
=3/31
2. be small and non-efficient:
= (46/93)*(14/46)
= 14/93
3. be an efficient van or efficient small car:
= (7/93) + (7/93)
= 14/93
4. be a non-efficient van:
= (46/93)*(2/46)
= 2/93
5. come from the large category is:
=11/93
Table 7 indicates that compact, large and sporty vans are generally more efficient as they have
more values above the mean than below. This is to say that small and midsize generally travel

17
less miles per gallon. This finding may be due to sampling error as the genertal expectation is
that small and midsize cars should travel more miles per gallon than vans because of their small
size.
Mpg best
Any car falling below the overall best mpg mean (29.09miles) found in appendix 7 is considered
non-efficient and any car falling above this overall best mpg mean is considered efficient.
Table 8:93 cars classified each in relation to the overall best mpgbeing either non-efficient
or efficientaccording carcategory.
Category Non- efficient Efficient Total
Compact 7 9 16
Small 11 10 21
Midsize 11 11 22
Large 6 5 11
Sporty 7 7 14
Van 4 5 9
Total 46 47 93
1. be compact and efficient is:
= (47/93)*(9/47)
= 3/31
2. be small and non-efficient:
= (46/93)*(11/46)
= 11/93
3. be an efficient van or efficient small car:
= (5/93) + (10/93)
= 15/93
4. be a non-efficient van:
= (46/93)*(4/46)
= 2/93
5. come from the large category is:
=11/93

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Table 8 shows that compact and van cars could be said to be more efficient than the other car
types because they have more cars over the mean than below (the difference is quite slight
though). For small, midsize and sporty cars there is a balance between the number of efficient
cars and inefficient cars. That is to say non-standard extras like customized engines (more
efficiency) or poor quality wheel alignment(less efficiency) could be the factors that cause any
significant difference.
Chi-Square Applications
Table 9: Observed and expected frequencies for low prices using basic price
Category Observed, fo Expected, fe
Compact 11 9.7
Small 21 9.7
Midsize 9 9.7
Large 0 9.7
Sporty 10 9.7
Van 7 9.7
Total 58 58.2
Steps
1. HO: fo=fe
H1: fo≠ fe
2. α = 5% level of significance.
The probability is 0.05 that the true null hypothesis will be rejected.
3. Chi- squared test statistic
4. Degrees of freedom=5, 0.05 significance level thus the critical value is 11.1 hence reject
null hypothesis if X2
c>11.1.
5. Table 10: Goodness of Fit Test
observed expected O - E (O - E)² / E % of chisq
11 9.700 1.300 0.174 0.73
21 9.700 11.300 13.164 55.20
9 9.700 -0.700 0.051 0.21
0 9.700 -9.700 9.700 40.67
10 9.700 0.300 0.009 0.04
7 9.700 -2.700 0.752 3.15
58 58.200 -0.200 23.849 100.00
23.85 chi-square

19
Since X2
c(23.85) according to table 10 is greater than the critical value (11.1) thus the null
hypothesis should be rejected. This means there is a less extreme number of low prices.
Table 11: Observed and Expected for High prices using basic price
Compact 5 5.8
Small 0 5.8
Midsize 13 5.8
Large 11 5.8
Sporty 4 5.8
Van 2 5.8
Total 35 34.8
Steps
1. HO: fo=fe
H1: fo≠ fe
c>11.1.
5. Table 12: Goodness of Fit test
5 5.800 -0.800 0.110 0.49
0 5.800 -5.800 5.800 25.71
13 5.800 7.200 8.938 39.62
11 5.800 5.200 4.662 20.67
4 5.800 -1.800 0.559 2.48
2 5.800 -3.800 2.490 11.04
35 34.800 0.200 22.559 100.00
22.56 chi-square
Since X2
hypothesis should be rejected. This means there is a less extreme number of high prices.

20
Table 13: Observed and Expected frequencies for low prices using top price
Compact 10 9.5
Small 21 9.5
Midsize 8 9.5
Large 5 9.5
Sporty 8 9.5
Van 5 9.5
Total 57 57
Steps
1. HO: fo=fe
H1: fo≠ fe
c>11.1.
10 9.500 0.500 0.026 0.14
21 9.500 11.500 13.921 74.51
8 9.500 -1.500 0.237 1.27
5 9.500 -4.500 2.132 11.41
8 9.500 -1.500 0.237 1.27
5 9.500 -4.500 2.132 11.41
57 57.000 0.000 18.684 100.00
18.68 chi-square
Since X2
hypothesis should be rejected. This means there is a less extreme number of low prices.

21
Table 15: Observed and Expected frequencies for high prices using top price
Compact 6 5.8
Small 0 5.8
Midsize 14 5.8
Large 5 5.8
Sporty 6 5.8
Van 4 5.8
Total 35 34.8
Steps
1. HO: fo=fe
H1: fo≠ fe
c>11.1.
6 5.800 0.200 0.007 0.04
0 5.800 -5.800 5.800 32.09
14 5.800 8.200 11.593 64.14
5 5.800 -0.800 0.110 0.61
6 5.800 0.200 0.007 0.04
4 5.800 -1.800 0.559 3.09
35 34.800 0.200 18.076 100.00
18.08 chi-square
Since X2
hypothesis should be rejected. This means there is a less extreme number of high prices.
The X2
c for low and high top prices are almost the same suggesting that the top prices are not
that different across vehicle categories.

22
Table 17: Observed and Expected frequencies for non-efficient using mpg town
Compact 7 7.7
Small 14 7.7
Midsize 12 7.7
Large 5 7.7
Sporty 6 7.7
Van 2 7.7
Total 46 46.2
Steps
1. HO: fo=fe
H1: fo≠ fe
3. Chi- square test statistic
c>11.1.
7 7.700 -0.700 0.064 0.48
14 7.700 6.300 5.155 39.17
12 7.700 4.300 2.401 18.25
5 7.700 -2.700 0.947 7.19
6 7.700 -1.700 0.375 2.85
2 7.700 -5.700 4.219 32.06
46 46.200 -0.200 13.161 100.00
13.16 chi-square
Since X2
hypothesis should be rejected. This means there is a less extreme number of miles travelled.

23
Table 19: Observed and Expected frequencies for efficient using mpg town
Compact 9 7.8
Small 7 7.8
Midsize 10 7.8
Large 6 7.8
Sporty 8 7.8
Van 7 7.8
Total 47 46.8
Steps
1. HO: fo=fe
H1: fo≠ fe
c>11.1.
5. Table 20:Goodness of Fit test
9 7.800 1.200 0.185 13.28
7 7.800 -0.800 0.082 5.90
10 7.800 2.200 0.621 44.65
6 7.800 -1.800 0.415 29.89
8 7.800 0.200 0.005 0.37
7 7.800 -0.800 0.082 5.90
47 46.800 0.200 1.390 100.00
1.39 chi-square
Since X2
c(1.39) according to table 20 is way below the critical value (11.1) thus the null
hypothesis should not be rejected. This means there are more of miles travelled within the
accepted region.

24
Table 21:Observed and Expected frequencies for efficient using mpg best
Category Obeserved, fo Expected, fe
Compact 7 7.7
Small 11 7.7
Midsize 11 7.7
Large 6 7.7
Sporty 7 7.7
Van 4 7.7
Total 46 46.2
Steps
1. HO: fo=fe
H1: fo≠ fe
c>11.1.
7 7.700 -0.700 0.064 1.25
11 7.700 3.300 1.414 27.68
11 7.700 3.300 1.414 27.68
6 7.700 -1.700 0.375 7.35
7 7.700 -0.700 0.064 1.25
4 7.700 -3.700 1.778 34.80
46 46.200 -0.200 5.109 100.00
5.11 chi-square
Since X2
c(5.11) referring to table 22 is below the critical value (11.1) thus the null hypothesis
should not be rejected. This means there are more of miles travelled within the accepted region.

25
Table 23: Observed and Expected frequencies for efficient using mpg best
Category Obeserved, fo Expected, fe
Compact 9 7.8
Small 10 7.8
Midsize 11 7.8
Large 5 7.8
Sporty 7 7.8
Van 5 7.8
Total 47 46.8
Steps
1. HO: fo=fe
H1: fo≠ fe
c>11.1.
9 7.800 1.200 0.185 4.38
10 7.800 2.200 0.621 14.74
11 7.800 3.200 1.313 31.18
5 7.800 -2.800 1.005 23.87
7 7.800 -0.800 0.082 1.95
5 7.800 -2.800 1.005 23.87
47 46.800 0.200 4.210 100.00
4.21 chi-square
Since X2
c(4.21) considering table 24 is below the critical value (11.1) thus the null hypothesis
should not be rejected. This means there are more of miles travelled within the accepted region.

26
Part 2 aim: Predicting mpg
Chart 1
Y = -0.072x + 32.74
Y = miles per gallon
X= horse power
2
r = -0.452
When: x= 0, y= 32.74
Y= 0, x= 454.72
There is a strong negative correlation, r, of -0.673 between horse power and miles per gallon.
The coefficient of determination,is 0.452. Therefore 45.2% of the variation in miles per gallon is
explained by the variation in horse power.54.8% of the variation is explained by other variables.
The negative gradient, -0.072 suggests that when HP increases, Mpg decreases, the higher the
horse power, the fewer the miles that can be travelled on one gallon of fuel.
y = -0.0722x + 32.746
R² = 0.4524
0
5
10
15
20
25
30
35
40
45
50
0 50 100 150 200 250 300 350
mpgtown
horse power (HP)
MPG Town v horse power
MPGTown
Linear (MPGTown)

27
Chart 2
Y= 32.62-3.846x
Y= miles per gallon
X= engine size
2
r = 0.5041
When X= 0, Y= 32.62
When Y=0, X= 8.48 (to 2 decimal places)
There is a strong negative correlation of -0.710 between engine size and miles per gallon. The
coefficient of determination is 0.5041 therefore, 50.41% of the variation in miles per gallon is
explained by the variation in the engine sizes.49.59% is explained by other variables. A negative
slope, -3.846 implies that when, engine size increases, mpg decreases.
y = -3.8464x + 32.627
R² = 0.5041
0
5
10
15
20
25
30
35
40
45
50
0.0 1.0 2.0 3.0 4.0 5.0 6.0
milespergallon(miles)
engine size (litres)
MPGTown vs engine size
MPGTown
Linear (MPGTown)

28
Chart 3
Y = 0.003x + 4.310
Y = mpg (town)
X = RMP
2
r = 0.131
Y = 0.003x + 4.310
= 0.003(0) + 4.310
= 0 + 4.310
= 4.310
There is a weak positive correlation of 0.362 between maximum revolutions of the engine per
minute and miles per gallon. The coefficient determination is 0.1318; therefore 13.18% of the
variation in MPG is explained by the variation in RMP. 86.82% is explained by other factors.
The positive gradient 0.003 suggests that when RMP increases, Mpg increases.
y = 0.0034x + 4.3109
R² = 0.1318
0
5
10
15
20
25
30
35
40
45
50
0 1000 2000 3000 4000 5000 6000 7000
MPG
RMP
Miles per gallon (MPG) Town v maximum
revolutions of enigine per minute (RMP)
MPGTown
Linear (MPGTown)

29
Chart 4
Y = -0.008x + 47.04
Y = mpg (town)
X= weight 2
r =
0.710 When:
x = 0, y = 47.04
y= 0, x = 57.08
There exists strong negative correlation, r of -0.842 between weight and miles per gallon. The
coefficient determination is 0.710, implying that 71% of the variation in miles per gallon is
accounted for by the variation in the weight of cars.29% is explained by other variables. The
gradient, -0.008 suggests an inverse relationship between weight and mpg, therefore when
weight increases, mpg decreases.
y = -0.008x + 47.048
R² = 0.7109
0
5
10
15
20
25
30
35
40
45
50
0 1000 2000 3000 4000 5000
Mpg(miles)
Weight (pounds)
Miles per gallon v weight
MPGTown
Linear (MPGTown)

30
Prediction of mpg
MPG (town) v horsepower (HP) – (refer to chart 2)
(i) When HP is 0, MPG is 32.74, which is the y-intercept.
(ii) Assuming that HP is 350, MPG will be 7.54. This implies that the equation can be
relied on, since it shows that when HP increases, MPG decreases. A one unit increase
in HP gives a 0.072 MPG decrease in efficiency.
(i) Y = 32.74 - 0.072x
= 32.74 – 0.072(0)
= 32.74
(ii) Y = 32.74 - 0.072x
= 32.74 - 0.072(350)
= 32.74 – 25.2
= 7.54
MPG (town) v length in inches (refer to chart 3)
Assuming the length of a car is 250 inches, MPG will be 5.34. This implies that the equation can
be relied on as it shows that when length increases MPG decreases. An increase of one inch,
results in a 0.256 MPG decrease in efficiency.
Y = 69.34 - 0.256x
= 69.34 - 0.256(250)
= 69.34 – 64
= 5.34

31
MPG (town) v engine size in litres - (refer to chart 4)
(i) When engine size = 0, MPG will be 32.62, which is the y-intercept.
(ii) Assuming a car has an engine size of, 6.0 litres, MPG will be 9.54 (to 2 decimal
places). This implies that the equation can be relied on as it shows that when engine
size increases MPG decreases. A 1 litre increase in engine size gives a 3.846 MPG
decrease in efficiency.
(i) Y= 32.62 - 3.846x
= 32.62 – 3.846(0)
= 32.62
(ii) Y = 32.62 - 3.846(6.0)
= 32.62 - 23.076
= 9.544
= 9.54 (to 2 decimal places)
MPG (town) v revolutions of engine per minute (RMP) - (refer to chart 5)
(i) When RMP = 0, MPG will be 4.310, which is the y-intercept.
(i) Assumimg that there are 7000 RMP, MPG will be 25.31. This implies that the
equation can be relied on, as it shows that when RMP increases, MPG increases. An
increase of 1 unit of RMP results in a 4.310 MPG increase in efficiency.
(ii) Y = 0.003x + 4.310
= 0.003(0) + 4.310
= 0 + 4.310
= 4.31 (to 2 decimal places)
(iii) Y = 4.310 +0.003x
= 4.310 + 0.003(7000)

32
= 4.310 + 21
= 25.31
MPG (town) v weight - (refer to chart 6)
Assuming that weight is 5000 pounds, MPG will be 7.04. This implies that the equation can be
relied on since it shows that an increase in weight results in a decrease in MPG. A 1 pound
increase in weight gives a 0.008 MPG decrease in efficiency.
Y = 47.04 - 0.008x
Y = 47.04 - 0.008(5000)
= 47.04 - 40
= 7.04

33
Chi-square application
Table 25:More passenger capacity
category Observed,f0 Expected,fe
compact 2 4.5
small 0 4.5
midsize 5 4.5
large 11 4.5
sporty 0 4.5
van 9 4.5
total 27 27
Steps
1. H0: fo = fe
H1: f0 ≠ fe
2. α = 5%. The probability is 0.05 that a true null hypothesis will be rejected.
3. Chi square test statistic
4. Degrees of freedom = 5, 0.05 significance level thus the critical value is 11.1 hence reject
c> 11.1.

34
5. Table 26: Goodness of Fit
Test
2 4.500 -2.500 1.389 5.71
0 4.500 -4.500 4.500 18.49
5 4.500 0.500 0.056 0.23
11 4.500 6.500 9.389 38.58
0 4.500 -4.500 4.500 18.49
9 4.500 4.500 4.500 18.49
27 27.000 0.000 24.333 100.00
24.33 chi-square
Since X2
c, (24.33)> 11.1 is greater than the critical value (11.1), the null hypothesis is rejected at
0.05 significance level.
Table 27: Less passenger capacity
category observed expected
compact 14 11
small 21 11
midsize 17 11
large 0 11
sporty 14 11
van 0 11
total 66 66
Steps
1. H0: fo = fe
H1: f0 ≠ fe
2. α = 5%. The probability is 0.05 that a true null hypothesis will be rejected.

35
3. Chi square test statistic
4. Degrees of freedom = 5, 0.05 significance level thus the critical value is 11.1 hence reject
c> 11.1.
5. Table 28: Goodness of Fit
Test
14 11.000 3.000 0.818 2.27
21 11.000 10.000 9.091 25.25
17 11.000 6.000 3.273 9.09
0 11.000 -11.000 11.000 30.56
14 11.000 3.000 0.818 2.27
0 11.000 -11.000 11.000 30.56
66 66.000 0.000 36.000 100.00
36.00 chi-square
Since X2
c, (36.00)> 11.1 is greater than the critical value (11.1), the null hypothesis is rejected at
0.05 significance level.

36
CONCLUSION
From the sample data of the 93 cars, the general aim was to analyze it and make different
conclusions of how the various car types are related to each other, whether there were any
similarities or differences, and what these differences meant relative to the population. The
analysis toolpak from excel was a great device in providing a fast way of having all the
desciptive statistics of the data at a go.
By use of the desciptive statistics various findings were made pertaining to the first aim which
was to show how car price differed by type of car. For example a discovery was made that
midsize cars were the most expensive cars across the car types and also that small cars were the
least expensive.
The second aim was to predict mpg and for this it was ascertained that most of the car
characteristics relative to the mpg had a negative gradient,. That is to say the proportion was
inverse, when the other variable of comparison (e.g. horsepower, engine size etc.) decreased mpg
increased. The only exception was the revolutions of the engine per minute which had a positive
slope. This means when the rpm’s increased the mpg also increased and vice versa.

37
BIBLIOGRAPHY
 Data analysis in business and management (Melanie Powell)
WORD COUNT
Pages 7
Words with numbers included 6811
Character (no spaces) 32659
Character (with spaces) 38522
Paragraphs 1498
Lines 2102
wlempadi

The last part of the analysis will examine the relationship between MPG and other variables in the data set and also look into the extent to which MPG can be predicted using the other variables.

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The last part of the analysis will examine the relationship between MPG and other variables in the data set and also look into the extent to which MPG can be predicted using the other variables.