Question

The average mpg usage for a 2009 Toyota Prius for a sample of 10 tanks of gas was 45.5 with a standard deviation of 1.8. For a 2009 Honda Insight, the average mpg usage for a sample of 10 tanks of gas was 42.0 with a standard deviation of 2.3.

Assuming equal variances, at α = .01, 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 > 2.552
b.	H0: μtoy – μhon ≤ 0 vs. H1: μtoy – μhon > 0. Reject H0 if tcalc < 2.552
c.	H0: μtoy – μhon ≥ 0 vs. H1: μtoy – μhon < 0. Reject H0 if tcalc < –2.552
d.	H0: μtoy – μhon ≥ 0 vs. H1: μtoy – μhon < 0. Reject H0 if tcalc > –2.552

(a-2)

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

  

tcalc

(a-3)	Based on the t-value 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

GIVEN:

Sample size of gas tankes for 2009 toyota prius

Sample average mpg usage for 2009 toyota prius

Sample standard deviation of mpg usage for 2009 toyota prius

Sample size of gas tankes for 2009 Honda Insight

Sample average mpg usage for 2009 Honda Insight

Sample standard deviation of mpg usage for 2009 Honda Insight  

LEVEL OF SIGNIFICANCE:

CRITICAL VALUE:

The right tailed t critical value with degrees of freedom at significance level is .

(a-1) HYPOTHESIS:

The correct hypothesis is Option (a):

(That is, the true mean mpg is higher for honda insight.)

(That is, the true mean mpg is lower for honda insight.)

Reject H₀ if

(a-2) TEST STATISTIC:

The t test statistic is,

where the pooled standard deviation is given by,

  

  

  

Now

Thus the t calculated value is

(a-3) DECISION RULE:

Reject H₀ if

Since the calculated t test statistic (3.7895) is greater than the t critical value (2.552), we reject the null hypothesis.

(a-4) CONCLUSION:

Since the calculated t test statistic (3.7895) is greater than the t critical value (2.552), we reject the null hypothesis and conclude that the true mean mpg is lower for honda insight.

(b) P VALUE:

We use the following function to calculate the p value

"=T.TEST(array1, array2,tails,type)"

array 1 refers to the first set of sample for 2009 Toyota Prius

array 2 refers to the second set of sample for 2009 Honda insight.

tails refers to whether 1 (one tailed) or 2 (two tailed test)

type takes the values:

1. the samples have paired values from the same population
2. the samples are from populations with the same variance
3. the samples are from populations with different variances

For our problem the correct excel function is ""=T.TEST(array1, array2,1,2)"

The p value is .

Since the p value is less than the significance level , we reject the null hypothesis and conclude that the true mean mpg is lower for honda insight.