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