Question

The average mpg usage for a 2009 Toyota Prius for a sample of 8 tanks of gas was 43.0 with a standard deviation of 1.4. For a 2009 Honda Insight, the average mpg usage for a sample of 8 tanks of gas was 41.0 with a standard deviation of 1.9.

Assuming equal variances, at α = 0.05, is the true mean mpg lower for the Honda Insight?

(a-1)

Choose the appropriate hypotheses.

a.	H0: μtoy – μhon ≤ 0 vs. H1: μtoy – μhon > 0. Reject H0 if tcalc > 1.761
b.	H0: μtoy – μhon ≤ 0 vs. H1: μtoy – μhon > 0. Reject H0 if tcalc < 1.761
c.	H0: μtoy – μhon ≥ 0 vs. H1: μtoy – μhon < 0. Reject H0 if tcalc < – 1.761
d.	H0: μtoy – μhon ≥ 0 vs. H1: μtoy – μhon < 0. Reject H0 if tcalc > – 1.761

(a-2)

Calculate the tcalc. (Round your answer to 4 decimal places.)

tcalc

(a-3)	Based on the tcalc determined, choose the correct decision.
	Fail to reject the null hypothesis Reject the null hypothesis

(a-4)	Is the true mean mpg lower for the Honda Insight?
	Yes No

(b)	Calculate the p-value using Excel. (Round your answer to 4 decimal places.)

p-value

Answer 1

a-1) The appropriate hypotheses are -

b. H0: μtoy – μhon ≤ 0 vs. H1: μtoy – μhon > 0

a-2) and a-3)

a-4) Yes.

b) To get P-value, Excel command : 1 - T.DIST(2.396886,12,TRUE)

Here,

P-value = 0.0169