hypotheses test in statistics using t-test

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[^]

http://www.foundasoft.com/index.php?option=com_content&view=article&id=84&Itemid=90[^]

Hope this help.