Do students tend to improve their SAT Mathematics (SAT-M) scores the second time they take the test? A random sample of four students who took the test twice received the following scores. Assume that the change in SAT-M score (second score - first score) for the population of all students taking the test twice is Normally distributed.What is a 90% confidence interval for ,the mean change in SAT-M score?

A) (-8.24,58.24)
B) (-18.08,68.08)
C) (-22.56,72.56)
D) (-39.31,89.31)

Question

Do students tend to improve their SAT Mathematics (SAT-M) scores the second time they take the test? A random sample of four students who took the test twice received the following scores.

Assume that the change in SAT-M score (second score - first score) for the population of all students taking the test twice is Normally distributed.What is a 90% confidence interval for ,the mean change in SAT-M score?

A) (-8.24,58.24)
B) (-18.08,68.08)
C) (-22.56,72.56)
D) (-39.31,89.31)

Ganga Sai Praveen Reddi · Accepted Answer

Final Answer : C, Explanation :  We need to use the formula for a confidence interval for a population mean:CI = sample mean +/- (t-value)(standard error)First, we need to find the sample mean and standard error:sample mean = (11+43+6+12)/4 = 18standard deviation = sqrt((11-18)^2 + (43-18)^2 + (6-18)^2 + (12-18)^2)/3 = 16.81standard error = standard deviation/sqrt(n) = 16.81/sqrt(4) = 8.405Next, we need to find the t-value. Since we have a sample size of 4, we have 3 degrees of freedom. Using a t-table or calculator, we find that the t-value for a 90% confidence interval with 3 degrees of freedom is 2.353.Plugging in all the values, we get:CI = 18 +/- (2.353)(8.405) = (-22.56, 72.56)Therefore, the best choice is (C), as it is the only choice that contains the correct confidence interval.

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