Question

In 1997, the average household expenditure for energy was $1,338, according to data obtained from the U.S. Department of Energy.  An economist claims that energy usage today is different from its 1997 level.  In a random sample of 36 households, the economist found the mean expenditure, adjusted for inflation, for energy in 2004 to be $1,423. with a sample standard deviation s = 360.

At a 95% level of confidence (α = .05), we wish to test the economists claim.

1. State the Null Hypothesis and Alternate Hypothesis for this experiment.

a.		Ho: p = $1,338 Ha: p not = $1,423
b.		Ho: µ <= $1,338 Ha: µ > $1,338
c.		Ho: µ = $1,423 Ha: µ not = $1,423
d.		Ho: µ = $1,338 Ha: µ not = $1,338

2.What is the p-value and decision of this research?

a.		p-value = .165; Do Not Reject Ho.
b.		p-value = .165; Reject Ho.
c.		p-value = .0825; Do Not Reject Ho.
d.		P-value = .0825; Reject Ho.

3.State the conclusion.

a.		With 95% Confidence, there is sufficient evidence to show that energy usage today is different from its 1997 level.
b.		With 95% Confidence, there is insufficient evidence to show that energy usage today is different from its 1997 level.
c.		With 95% Confidence, there is sufficient evidence to show that energy usage today is greater than its 1997 level.
d.		With 95% Confidence, there is insufficient evidence to show that energy usage today is greater than its 1997 level.

4.State the Type I error for this Hypothesis Test and the corresponding probability of a Type I error occurring in this experiment.

a.		Conclude energy usage is not different, but it really is. Probability = .05
b.		Conclude energy usage is not different, but it really is. Probability = .95
c.		Concluded energy usage is different, but it really isn't. Probability = .95
d.		Conclude energy usage is different, but it really isn't. Probability = .05

5.In order to decrease the probability of a Type I error, we would do the following before conducting this experiment:

a.		Increase the Confidence Level of the Hypothesis Test, thereby decreasing alpha.
b.		Decrease the Confidence Level of the Hypothesis Test, thereby decreasing alpha.
c.		Increase the sample size from 36.
d.		Decrease the sample size from 36.

Answer 1

1 to 3:

3) option B

With 95% Confidence, there is insufficient evidence to show that energy usage today is different from its 1997 level.

4) D

Conclude energy usage is different, but it really isn't. Probability = .05 5) On the opposite, too large samples increase the type 1 error because the p-value depends on the size of the sample, but the alpha level of significance is fixed. A test on such a sample will always reject the null hypothesis C option Increase the sample size from 36.