When using a one-sample t-procedure to construct a confidence interval for the mean of a finite population, a condition is that the population size be at least 10 times the sample size. The reason for the condition is to ensure that the sample size is large enough the sample size is large enough A the central limit theorem is applicable for the sample mean the central limit theorem is applicable for the sample mean B the sample standard deviation is a good approximation of the population standard deviation the sample standard deviation is a good approximation of the population standard deviation C the degree of dependence among observations is negligible the degree of dependence among observations is negligible D the sampling method is not biased

C. The degree of dependence among the observation is negligible.

Step-by-step explanation:

The conditions for performing a t-procedure when constructing a t-interval are;

1) The samples observation should be independent of each other

2) The use of a random sample or experiment for the procedure

3) Ensure the normality of the data of the dependent variable

Given that surveys usually involve sampling without replacement from a population which is finite can not be taken as independent Bernoulli trials however, it is allowable to still consider samples independent when they are less than 10% the size of population

Therefore, the reason for the condition is to ensure that the population to sample size ratio is large enough and that the degree of dependence among the observation is negligible.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.