Let X1, X2, ... , X5 be a random sample of SAT mathematics scores, assumed to be N(X

Chapter 7, Problem 7.2-2

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QUESTION:

Let \(X_{1}, X_{2}, \ldots, X_{5}\) be a random sample of SAT mathematics scores, assumed to be \(N\left(\mu_{X}, \sigma^{2}\right)\), and let \(Y_{1}, Y_{2}, \ldots, Y_{8}\) be an independent random sample of SAT verbal scores, assumed to be \(N\left(\mu_{Y}, \sigma^{2}\right)\). If the following data are observed, find a 90% confidence interval for \(\mu_{X}-\mu_{Y}\):

\(\begin{array}{lllll} x_{1}=644 & x_{2}=493 & x_{3}=532 & x_{4}=462 & x_{5}=565 \\ y_{1}=623 & y_{2}=472 & y_{3}=492 & y_{4}=661 & y_{5}=540 \\ y_{6}=502 & y_{7}=549 & y_{8}=518 & & \end{array}\)

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QUESTION:

Let \(X_{1}, X_{2}, \ldots, X_{5}\) be a random sample of SAT mathematics scores, assumed to be \(N\left(\mu_{X}, \sigma^{2}\right)\), and let \(Y_{1}, Y_{2}, \ldots, Y_{8}\) be an independent random sample of SAT verbal scores, assumed to be \(N\left(\mu_{Y}, \sigma^{2}\right)\). If the following data are observed, find a 90% confidence interval for \(\mu_{X}-\mu_{Y}\):

\(\begin{array}{lllll} x_{1}=644 & x_{2}=493 & x_{3}=532 & x_{4}=462 & x_{5}=565 \\ y_{1}=623 & y_{2}=472 & y_{3}=492 & y_{4}=661 & y_{5}=540 \\ y_{6}=502 & y_{7}=549 & y_{8}=518 & & \end{array}\)

ANSWER:

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A confidence interval is a statistical concept that provides a range of values within which we can be reasonably confident that the true value of a population parameter lies. It is used to quantify the uncertainty or margin of error associated with an estimate.

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