Question

Is there a significant difference in mean Highway MPG between expensive and cheap cars?

I understand that I must conduct a hypothesis test and confidence interval for two means. I have found the mean for cheap cars to be 33.6, the standard deviation 5.57; the mean for expensive cars 26.1, the standard deviation 2.14. Please use both the critical values method and p-value method to determine if there is a significant difference. Be mindful of outliers (cheap cars outlier=50, expensive car outlier=22), how should we explain this?

Price_Category | HighwayMPG | Price_Category | HighwayMPG | |

Cheap | 34 | Expensive | 25 | |

Cheap | 46 | Expensive | 25 | |

Cheap | 36 | Expensive | 24 | |

Cheap | 33 | Expensive | 25 | |

Cheap | 50 | Expensive | 23 | |

Cheap | 30 | Expensive | 30 | |

Cheap | 43 | Expensive | 26 | |

Cheap | 37 | Expensive | 24 | |

Cheap | 33 | Expensive | 25 | |

Cheap | 37 | Expensive | 29 | |

Cheap | 26 | Expensive | 27 | |

Cheap | 41 | Expensive | 25 | |

Cheap | 30 | Expensive | 26 | |

Cheap | 33 | Expensive | 30 | |

Cheap | 31 | Expensive | 28 | |

Cheap | 36 | Expensive | 28 | |

Cheap | 33 | Expensive | 26 | |

Cheap | 26 | Expensive | 30 | |

Cheap | 31 | Expensive | 22 | |

Cheap | 38 | Expensive | 24 | |

Cheap | 37 | Expensive | 28 | |

Cheap | 30 | Expensive | 26 | |

Cheap | 33 | Expensive | 26 | |

Cheap | 29 | Expensive | 26 | |

Cheap | 34 | Expensive | 25 | |

Cheap | 33 | Expensive | 28 | |

Cheap | 27 | Expensive | 26 | |

Cheap | 30 | Expensive | 28 | |

Cheap | 27 | Expensive | 25 | |

Cheap | 29 | Expensive | 26 | |

Cheap | 36 | Expensive | 22 | |

Cheap | 33 | |||

Cheap | 27 |

Answer #1

Two-sample T for HighwayMPG

Price_Category N Mean StDev SE
Mean

Cheap
33 33.61 5.57 0.97

Expensive 31 26.06
2.14 0.39

Difference = μ (Cheap) - μ (Expensive)

Estimate for difference: 7.54

95% CI for difference: (5.41, 9.68)

T-Test of difference = 0 (vs ≠): T-Value = 7.06 P-Value = 0.000 DF
= 62

Both use Pooled StDev = 4.2725

TS = 7.06 > critical value

we reject the null hypothesis

similarly

p-value = 0.000 < 0.05

we reject the null hypothesis

we conclude that there is a significant difference in mean Highway MPG between expensive and cheap cars

Is there a significant difference in mean Highway MPG between
expensive and cheap cars?
I understand that I must conduct a hypothesis test and
confidence interval for two means. I have found the mean for cheap
cars to be 33.6, the standard deviation 5.57; the mean for
expensive cars 26.1, the standard deviation 2.14. Please use the
appropriate formulas in order to determine if there is a
significant difference.
Price_Category
HighwayMPG
Price_Category
HighwayMPG
Cheap
34
Expensive
25
Cheap
46
Expensive...

Dataset:
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53 50
38 34
46 44
30 36
31 23
26 31
29 25
48 51
65 46
29 26
28 23
29 32
25 22
22 21
21 24
43 50
24 27
38 33
33 26
35 29
40 29
27 25
27 24
49 38
48 39
27 27
26 24
40 34
35 37
21 26
32 39
30 28
60 52
36 40
25 23
66 55
52 34
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