State What the Given Confidence Interval Suggests About the Two

question 192

Multiple Choice

State what the given confidence interval suggests about the two population means.
-A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs. $$\begin{array} { | c | c c | } \hline \text { College A } & \text { College B } \\\hline 3.7 & 3.8 & 2.8 \\3.2 & 3.2 & 4.0 \\3.0 & 3.0 & 3.6 \\2.5 & 3.9 & 2.6 \\2.7 & 3.8 & 4.0 \\3.6 & 2.5 & 3.6 \\2.8 & 3.9 & \\3.4 & & \\\hline\end{array}$$ Construct a 95% confidence interval for the difference between the mean GPA of college A students and the
Mean GPA of college B students. (Note: $\bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , s _ { 1 } = 0.4357 , \mathrm {~s} _ { 2 } = 0.5485$ .)

• A) \(- 0.91 < \mu _ { 1 } - \mu _ { 2 } < 0.25\)
• B) \(- 0.65 < \mu _ { 1 } - \mu _ { 2 } < - 0.01\)
• C) \(- 0.81 < \mu _ { 1 } - \mu _ { 2 } < 0.15\)
• D) \(- 0.72 < \mu _ { 1 } - \mu _ { 2 } < 0.07\)

Understand regression toward the mean and its implications for performance and prediction.

Grasp the importance of sample size and variability in accurate estimation of population parameters.

Recognize how sample size and variability affect the likelihood of observing differences between sample means.

Understand the role of standard deviations in determining statistical significance of sample group differences.

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Definitions:

Direct Labor Time

Direct labor time is the amount of time spent by workers directly involved in the production of goods or services, excluding time of indirect labor like maintenance or supervision.

Direct Materials Budget

A financial plan that estimates the raw materials needed for production and the associated costs.

Production Budget

An estimate of the number of units that must be produced during a period to meet expected sales demand and to satisfy ending inventory requirements.

Raw Materials

These are the basic, unprocessed inputs used in manufacturing to produce finished goods.