Question

Who are better drivers’ males or females?

Here are some relevant statistics from the data in 2015:

Drivers	Total Involved Drivers	Drivers in Fatal Collisions	Drivers in Serious Injury Collisions	Drivers in Minor Injury Collisions	Drivers in Property Damage Only Collisions	Drivers in Unknown Injury Collisions
Males	114,297	541	1,751	35,374	75,742	889
Females	81,924	226	790	27,901	52,425	582
Total	196,221	767	2,541	63,275	128,167	1,471

a) Exploratory Data Analysis

• Presence of data analysis and graphs
• Discussion of results and how this led to claim

b) Hypothesis test elements   

• Claim, null, alternative, significance level
• Test stat formula and result including p-value
• Graph, critical value and region, comparison with stat and p-value
• Conclusion
• Interpretation

Answer 1

Step -1: State the hypothesis:

Null hypothesis: H0: Males are better drivers

Alternative hypothesis: H1: Females are better drivers

Step-2: Observed Frequencies:

Drivers	Drivers in Fatal collision	Drivers in seriously injured collision	Drivers in minor injury collision	Drivers in property damage only collision	Drivers in unknown injury collision	Total
Male	541	1751	35374	75742	889	114297
Female	226	790	27901	52425	582	81924
Total	767	2541	63275	128167	1471	196221

Step-3:Expected Frequencies:

Fe11 = (114297   x 767 ) / 196221 = 446.7707

Fe12 = (114297 x 2541 ) / 196221 = 1480.1101

Fe13 = (114297   x 63275 ) / 196221 = 36857.1288

Fe14 = (114297   x 128167 ) / 196221 = 74656.1459

Fe15 = (114297    x 1471 ) / 196221 = 856.8445

Fe21 = ( 81924     x 767 ) / 196221 = 320.2293

Fe22 = (81924      x 2541 ) / 196221 = 1060.8899

Fe23 = (81924    x 63275 ) / 196221 = 26417.8712

Fe24 = (81924    x 128167 ) / 196221 = 53510.8541

Fe25 = (81924    x 1471 ) / 196221 = 614.1555

Drivers	Drivers in Fatal collision	Drivers in seriously injured collision	Drivers in minor injury collision	Drivers in property damage only collision	Drivers in unknown injury collision	Total
Male	446.7707	1480.1101	36857.1288	74656.1459	856.8445	114297
Female	320.2293	1060.8899	26417.8712	53510.8541	614.1555	81924
Total	767	2541	63275	128167	1471	196221

Step-4: Compute Chi-square:

χ2 = ∑ [ (Oi - Ei)² / Ei ]

= (541 - 446.7707)²/ 446.7707 + (1751 - 1480.1101)²/ 1480.1101 + (35374 -36857.1288)²/    36857.1288 + (75742 - 74656.1459)²/ 74656.1459 + (889 - 856.8445)²/ 856.8445 +  
(226 - 320.2293)²/ 320.2293 + (790 - 1060.8899)²/ 1060.8899 + (27901 -26417.8712)²/ 26417.8712 + (52425 - 53510.8541)²/ 53510.8541 + (582 - 614.1555)²/ 614.1555

= 19.8741+49.5783+59.681+15.7935+1.2067+27.7275+69.1696+83.2645+22.0344+1.6836

= 350.0132

χ2 = 350.0132       -------------------------(Calculated value)

Step-5: Compute the degrees of freedom (df):
df= (2 - 1)⋅(5 - 1)

df = 4
Level of significance = 0.05

χ2 = 9.488      -------------------------(Tabulated value)

Step-6: Decision:

Calculated value > Tabulated value

350.0132   > 9.488

Step-7: Conclusion:

Null hypothesis is rejected.

Alternative hypothesis is accepted.

H1: Females are better drivers

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If we take the percentage of their scores we get the following result

Male	0.47%	1.53%	30.94%	66.26%	0.77%
Females	0.27%	0.96%	34.05%	64%	0.71%

From table it is clear that the males percentage are higher than the females percentage.

It means more accidents are happened in case of males.

Therefore, In this cases Females are better drivers.