I assume you have a sample of size 7 and assume those values are sold prices from a fixed value, zero(your dummy). You get an average of 591.9 with a "big" standard deviation of 269.3, which is the square root of 72542.5. You may have some individual value more than 700 and some less than 700, but all centering at 591.9. At a glance, sample mean (=591.9) may make you think that the population may have sold price less than 700. But you want to conclude in a more objective way, e.g. using hypothesis testing.
So now you want to use your
sample results to draw an
inference about the
population that the population has sold price (i) not equal to 700, or (ii) more than 700, or (iii) less than 700.
From your results, I can see that you are using paired t test.
Coincidentally, I have developed some Excel Stat tool that serve the above purpose. Following is the result i get from using the Excel Stat tool. It answers your question (a) to (d).
Two-Samples Paired t-Test
Sample Size = 7
Average Difference= 591.857
Stdev. of Difference= 269.3371
Significance Level(alpha)= 0.05
Hypothesized Difference = 700
Test Statistics -1.0623
H0 : µ1-µ2 = 700 H0 : µ1-µ2 >= 700 H0 : µ1-µ2 <= 700
H1 : µ1-µ2 != 700 H1 : µ1-µ2 < 700 H1 : µ1-µ2 > 700
or or or
H0 : µD = 700 H0 : µD >= 700 H0 : µD <= 700
H1 : µD != 700 H1 : µD < 700 H1 : µD > 700
2-Tailed 1-Tailed Left 1-Tailed Right
Critical t Value ±2.4469 -1.943180281 1.943180281
p-value 0.3290 0.1645 0.8355
Conclusion Not Reject H Null Not Reject H Null Not Reject H Null
There are 3 columns. Left column for not equal to 700, middle column for less than 700, and right column for more than 700.
For your question (a), it can be shown in 3 ways namely, not equal to 700, less than 700, and more than 700. µ1 is the mean of sold price, µ2 is the mean of dummy, and µD is the mean of differences.
For question (b - d), it depends on what do you test on. Again I assume you want to show that sold price of population is
less than 700 (one-tailed test, see middle column). Your results show that alpha you use is 0.05.
Using p-value, it is 0.1645 which is more than 0.05, so conclusion is: Not reject H null, that means Not reject sold price =700. Inference is: population sold price is
not less than 700 (but we "dare" not say sold price is 700 or more, because not rejecting null hypothesis is a "weak" statement).
Using t value, reject area is less than -1.943, and your t stat is -1.0623 which is not fall in reject area, thus not reject H null.
Sad to say that although you cannot say sold price is less than 700, but you do not have strong evidence showing that sold price is 700. Hypothesis testing is "good" for rejecting, not the opposite. This happen due to the big value of standard deviation.
Another method. You can also conduct a one-sample t test. See the following Excel results.
One-Sample t-Test
Hypothesized miu = 700
Sample size = 7
Sample Mean = 591.857
Sample Stdev.= 269.3371
Significance Level = 0.05
Test Statistics = -1.06
H0 : µ =700 H0 : µ >=700 H0 : µ <=700
H1 : µ !=700 H1 : µ < 700 H1 : µ > 700
2-Tailed 1-Tailed Left 1-Tailed Right
Critical t Value ±2.4469 -1.9432 1.9432
p-value 0.3290 0.1645 0.8355
Conclusion Not Reject H Null Not Reject H Null Not Reject H Null
You will get similar conclusions
You can go to below link to get a copy of Excel add-in tool for above purpose.
http://www.foundasoft.com/index.php?option=com_wrapper&view=wrapper&Itemid=94[
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http://www.foundasoft.com/index.php?option=com_content&view=article&id=84&Itemid=90[
^]
Hope this help.