Question

A manufacturer claims that the mean driving per mile of its sedans is less than that of its leading competitor. You conduct a study using 28 randomly selected sedans from the manufacturer and 32 from the leading competitor. The results are given below

Sample statistics for Sedan Driving Costs

Manufacturer	Competitor
X1 = 0.48 /mi	X2 = 0.5 /mi
s1 = 0.05 /mi	s2 = 0.07 /mi
n1 = 28	n2 = 32

3. What is the pooled standard deviation?

4. Observed test statistic

5. The degrees of freedom for the test statistic

Tries 0/5

6. P-value:

Tries 0/5

Answer 1

3)

Pooled Std.dev
sp = sqrt((((n1 - 1)*s1^2 + (n2 - 1)*s2^2)/(n1 + n2 - 2))*(1/n1 + 1/n2))
sp = sqrt((((28 - 1)*0.05^2 + (32 - 1)*0.07^2)/(28 + 32 - 2))*(1/28 + 1/32))
sp = 0.0159

4)

Test statistic,
t = (x1bar - x2bar)/sp
t = (0.48 - 0.5)/0.0159
t = -1.258

5)

df = n1 + n2 - 2 = 58

6)

P-value Approach
P-value = 0.1067