## The Implementation of Applied Statistics in the Car Manufacturing Industry

### Descriptive statistics

### Graphs and Descriptive Statistics

From this box plot of Acceleration of cars categorized by different origins, we can Median Acceleration is more for Japan than Europe than the US. But Acceleration has more variation across cars in Europe than in the US than in Japan.

From the Scatterplot of the weight of car and Horsepower of car, we can see a trend that the Horsepower of the car increases with an increase in weight of the car.

From this box plot of Horsepower of cars categorized by different origins, we can Median Horsepower is more for the US than Europe than Japan. But Horsepower has more variation across cars in the US than in Japan than in Europe.

From the Scatterplot of miles per gallon of car and Horsepower of car, we can see a trend that Miles per gallon of the car decreases with an increase in Horsepower of car.

Mean of acceleration | ||

Europe | Japan | US |

16.8219 | 16.17215 | 14.94252 |

the standard deviation of acceleration | ||

Europe | Japan | US |

3.01092 | 1.954937 | 2.804542 |

Frequency Table between Origin and Cylinder type in cars | |||

Europe | Japan | US | |

high | 0 | 0 | 108 |

low | 69 | 73 | 72 |

medium | 4 | 6 | 74 |

Mean of Horsepower | ||

Europe | Japan | US |

78.78082 | 79.83544 | 118.0118 |

the standard deviation of Horsepower | ||

Europe | Japan | US |

24.4627 | 17.8192 | 42.39793 |

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### Hypothesis Testing

**Null Hypothesis:**Mean acceleration for cars is the same across cars of all origins

**Alternate Hypothesis:** Mean acceleration is different for cars of at-least one origin than others.
Single-factor ANOVA Result

ANOVA Table Origin and Acceleration | |||||

Df | Sum Sq | Mean Sq | F-value | P-value | |

Origin | 2 | 242 | 121 | 16.58 | 0.00E+00 |

Residuals | 403 | 2941 | 7.3 |

**Null Hypothesis:** Origin of car and type of Cylinder are independent of each other.
**Alternate Hypothesis: **Origin of car and type of Cylinder are not independent of each other.
Chi-Square test of independence between categorical variables.

Pearson's Chi-squared test | ||

X-squared = 164.52 | df = 4 | p-value =0 |

**Conclusion**-Since the p-value is less than 0.05 we can reject the Null hypothesis at a significance level of 0.05 and conclude that we have significant evidence that the Origin of the car and type of Cylinder is not independent of each other.

**Null Hypothesis: **There is no relationship between the weight of a car and horsepower.i.e correlation coefficient is 0.

**Alternate Hypothesis:**There is a relationship between the weight of a car and horsepower.The correlation coefficient is different from 0.

correlation between weight and Horsepower |

0.8408106 |

t = 31.22 | df = 404 | p-value =0 |

**Conclusion**-Since the p-value is less than 0.05 we can reject the Null hypothesis at a significance level of 0.05 and conclude that we have significant evidence that there is a relationship between the weight of a car and horsepower. That meansthe correlation coefficient is significantly different from 0.

**Null Hypothesis:**There is no relationship between Miles per gallon and horsepower .i.e correlation coefficient is 0.

**Alternate Hypothesis:**There is a relationship between Miles per gallon and horsepower.The correlation coefficient is different from 0.

correlation between Miles per gallonand Horsepower |

-0.7267 |

t = -21.261 | df = 404 | p-value =0 |

**Conclusion**-Since p-value is less than 0.05 we can reject the Null hypothesis at a significance level of 0.05 and conclude that we have significant evidence that there is a relationship between Miles per gallon and horsepower. That meansthe correlation coefficient is significantly different from 0.

**Null Hypothesis:** Mean Horsepower for cars is the same across cars of all origins
**Alternate Hypothesis:** Mean Horsepower is different for cars of at-least one origin than others.
Single-factor ANOVA Result

ANOVA Table for Origin and Horsepower | |||||

Df | Sum Sq | Mean Sum Sq | F | P-value | |

Origin | 2 | 142337 | 71168 | 54.88 | 0 |

Residuals | 403 | 522642 | 1297 |

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