Comprehensive Statistical Analysis of Vehicle Usage Data

This assignment provides a comprehensive statistical analysis of vehicle data collected through a survey. The analysis begins with descriptive statistics of miles driven, broken down by gender and vehicle type, followed by hypothesis testing. A one-sample t-test is used to determine if the average miles driven per month differs from a national average. Binomial tests are employed to compare the proportions of domestic and foreign vehicles driven, and to compare these proportions across genders. Independent samples t-tests are used to assess whether there are significant differences in miles driven between males and females, both overall and for specific vehicle types. Finally, a one-way analysis of variance (ANOVA) is performed to compare the average miles driven across different vehicle types, along with the necessary assumptions and their validity. The assignment concludes with the interpretations of the statistical results and conclusions drawn from the analysis.

Miles driven from work
Gender Vehicle Driven
Mea
n Std. Deviation Minimum Maximum
Female Car 18.89 13.237 0 45
Mini Van 3.33 6.172 0 15
SUV 24.25 10.846 17 50
Total 14.36 13.532 0 50
Male Car 19.29 7.804 10 35
Mini Van 12.43 12.435 0 30
SUV 24.47 8.983 15 45
Total 20.31 10.563 0 45
Question 2: According to the US Department of Transportation Federal Highway
Administrations, Americans drive an average of 13,476 miles per year . This translates to 1123 miles per
month. Based on the data collected, is there evidence that Americans drive an average of 1123 miles
per month?
H0: Americans do not drive an average of 1123 miles per month
H1: Americans drive an average of 1123 miles per month
The most appropriate test that applies to this problem is one sample t test, we will pick the p value of t
test statistic and compare with 5%.
One-Sample Test
Test Value = 1123
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the
Difference
Lower Upper
Miles from work -735.591 70 .000 -1106.211 -1109.21 -1103.21
The p value obtained as shown in the table is 0.0000 which is less than 0.05 thus H0is rejected at
5%, thus there is enough evidence to conclude that Americans drive more than 1123 miles per month.
Question 3: The auto industry believes that more domestic vehicles than foreign vehicles are driven by
the US population in general. Based on the data collected,
Is there evidence that the proportion of domestic vehicles driven is greater than that of foreign vehicles
driven?
Ho: proportion of domestic vehicles driven is the same as that of foreign vehicles driven
H1: the proportion of domestic vehicles driven is greater than that of foreign vehicles driven

Binomial Test
Category N Observed Prop. Test Prop. Sig. (2-tailed)
Vehicle Type
Group 1 Foreign 28 .39 .50 .096
Group 2 Domestic 43 .61
Total 71 1.00
From the binomial test of proportionality table above, the p value=0.096>0.05, thus we fail to
reject H0 and conclude there is no enough evidence to support that proportion of domestic
vehicles is greater than foreign.
Is there evidence that the proportion of domestic vehicles driven by males is greater than that of foreign
vehicles driven by males?
H0: the proportion of domestic vehicles driven by males is the same as that of foreign vehicles driven by
males.
H1: the proportion of domestic vehicles driven by males is greater than that of foreign vehicles driven by
males
Binomial Test
Category N Observed Prop. Test Prop. t Sig. (2-tailed)
Vehicle Type
Group 1 Domestic 21 .72 .50 .024
Group 2 Foreign 8 .28
Total 29 1.00
The p value of binomial test of proportionality =0.024<0.05, we reject H0, thus there is enough
evidence to conclude that proportion of domestic vehicles driven by male is greater than that for
foreign.
Is there evidence that the proportion of domestic vehicles driven by females is greater than that of
foreign vehicles driven by females?

H0: The proportion of domestic vehicles driven by females is the same as that of foreign vehicles driven
by females.
H1: the proportion of domestic vehicles driven by females is greater than that of foreign vehicles driven
by females
Binomial Test
Category N Observed Prop. Test Prop. Exact Sig. (2-
tailed)
Vehicle Type
Group 1 Foreign 20 .48 .50 .878
Group 2 Domestic 22 .52
Total 42 1.00
The binomial test of proportionality yields p value =0.878>0.05, thus we fail to reject H0 and conclude
that there is no enough evidence to conclude that the proportion of domestic vehicles driven by females
is greater than that of foreign vehicles driven by females.
Question 4: The Federal Highway Administration reported that men drive more miles than
women. Based on the data provided, is there sufficient evidence that on average males drive more
miles than females for:
• all vehicles drive
h0: on average males drive same miles than females for all vehicles drive
H1: on average males drive more miles than females for all vehicles drive
The two
independent t
test applied
yields p
value=0.069>0.05. Thus, we fail to reject H0, we therefore conclude that there is no enough evidence to
conclude that on average, male drive more miles than females.
Independent Samples Test
Levene's Test for
Equality of Variances t-test for Equality of Means
F Sig. t df
Sig. (2-
tailed)
Miles
driven per
month
Equal
variances
assumed
3.414 .069 1.147 69 .255
Equal
variances
not
assumed
1.111 53.414 .271

• SUV
Independent Samples Test
Levene's Test for
Equality of Variances
F Sig. t df
Miles
driven
per
month
Equal
variance
s
assumed
3.414 .069 1.147 69
Equal
variance
s not
assumed
1.111 53.414
• Mini Van
Female Male
Mean 766
557.142
9
Variance 56154.28571
11323.8
1
Observations 15 7
Pooled Variance 42705.14286
Hypothesized Mean Difference 0
df 20
t Stat 2.207966868
P(T<=t) one-tail 0.0195442
t Critical one-tail 1.724718243
P(T<=t) two-tail 0.0390884
t Critical two-tail 2.085963447
• Car
Ho:

Levene's Test for
Equality of Variances
t-test for
Equality
of Means
F Sig. t
Miles
driven
per
month
Equal
variances
assumed
.685 .416 -.657
Equal
variances
not
assumed
-.722
Question 5: The leasing company is interested in comparing the average miles driven across the three
vehicles captured in the survey. What test would you use to test the differences in average monthly
miles driven across the vehicles driven? One-way analysis of variance
What assumptions are needed for you to perform this test?
 Presence of replications and randomness
 Observations made independently
 Error terms normally distributed.
Are the assumptions valid for you to conduct the test? YES
Provide evidence.
The appearance of cars is more than one and appeared randomly thus the first assumption is met.
Appearance of a certain type of car do not influence appearance of another type thus independency

The bell shaped curve depict that normality was met.
If appropriate, perform the hypotheses test to determine if the average miles driven across the vehicles
used are different. If differences exist, determine which pair of vehicles miles driven
are different. Make sure to state your null and alternate hypotheses.
Use a significant value of 5% for your test. What conclusions would you deduce from your analysis?