Sat practice Test #8 Answer Explanations

Choice C is correct. In order to use a sample mean to estimate 
the mean for a population, the sample must be representative of 
the population (for example, a simple random sample). In this 
case, Tabitha surveyed 20 families in a playground. Families in the 
playground are more likely to have children than other households 
in the community. Therefore, the sample isn’t representative of the 
population. Hence, the sampling method is flawed and may produce 
a biased estimate.
Choices A and D are incorrect because they incorrectly assume the 
sampling method is unbiased. Choice B is incorrect because a sample 
of size 20 could be large enough to make an estimate if the sample had 
been representative of all the families in the community.
QUESTION 27
Choice B is correct. Since the point (p, r) lies on the line with equation 
y = x + b, the point must satisfy the equation. Substituting p for x and 
r for y in the equation y = x + b gives r = p + b. Similarly, since the 
point (2p, 5r) lies on the line with the equation y = 2x + b, the point 
must satisfy the equation. Substituting 2p for x and 5r for y in the 
equation y = 2x + b gives 5r = 2(2p) + b, or 5r = 4p + b. Solving each 
equation for b gives b = r − p and b = 5r − 4p, respectively. Substituting 
r − p for b in the equation b = 5r − 4p gives r − p = 5r − 4p. Subtracting 
r from each side of the equation and adding 4p to each side of the 
equation gives 3p = 4r. Dividing each side of the equation by p and 
dividing each side of the equation by 4 gives 3 
_ 
4 =
r 
_ 
p .
Choices A, C, and D are incorrect. Choices A and D may be the result 
of incorrectly forming the answer out of the coefficients in the point 
(2p, 5r). Choice C may be the result of confusing r and p.

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QUESTION 28