Homework SourseYou wish to determine whether an energyusage awareness campa
You wish to determine whether an energy-usage awareness campaign has a significant impact on the amount of electricity used per day by households. You randomly select a sample of eight households in a particular residential area, and measure their daily eclectricity usage (in kw hours) both before and after exposure to the campaign. The results are given in the table below:
Daily Electricity Usage(kw Hours)
Household Before Campaign After Campaign
Perform an appropraite test at the 5% significant level to determine whether exposure to the campaign has a significant impacct upon daily electricity usage by households. Show all calculations, by hand and MS Excel.
| 1 | 29 | 29 |
|---|---|---|
| 2 | 25 | 25 |
| 3 | 22 | 22 |
| 4 | 21 | 20 |
| 5 | 22 | 22 |
| 6 | 26 | 25 |
| 7 | 24 | 22 |
| 8 | 28 | 26 |
Solution
Let ud = u2 - u1.
Formulating the null and alternative hypotheses,
Ho: ud = 0
Ha: ud =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the standard deviation of the differences (third column):
s = 0.797724035
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 0.301511345
Calculating the mean of the differences (third column):
XD = -0.857142857
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = -2.842821249
As df = n - 1 = 6
Then the critical value of t is
tcrit = +/- 2.446911851
As |t| > 2.4469, WE REJECT THE NULL HYPOTHESIS.
Also, using p values, as it is 2 tailed,
p = 0.029457688
Also, as P < 0.05, WE REJECT THE NULL HYPOTHESIS.
Thus, there is a significant impact on the amount of electricity used per day by households. [CONCLUSION]
