Question

# Is there a significant difference in mean Highway MPG between expensive and cheap cars? I understand...

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

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

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