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 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	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

Here we have two independent samples so independent sample t test will be used. Hypotheses are:

Following is the sample mean and sample SD:

	Cheap	Expensive
mean	33.61	26.06
std. dev.	5.57	2.14
n	33	31

So we have

Since it is not given that variances are equal so degree of freedom of the test is

So df is 41.

Test is two tailed so critical values for , using excel function "=TINV(0.05,41)", are +/-2.020. Rejection region:

If t < -2.020 or t > 2.020, reject H0

The test statistics will be

Since test statistics lies in the rejection region so we reject the null hypothesis. That is we can cocnlude that there is a significant difference in mean Highway MPG between expensive and cheap cars.