A reading exam is given to the sixth graders at three
Chapter 10, Problem 128SE(choose chapter or problem)
A reading exam is given to the sixth graders at three large elementary schools. The scores on the exam at each school are regarded as having normal distributions with unknown means \(\mu_{1}, \mu_{2}\), and \(\mu_{3}\), respectively, and unknown common variance \(\sigma^{2}\left(\sigma_{1}^{2}=\sigma_{2}^{2}=\sigma_{3}^{2}=\sigma^{2}\right)\). Using the data in the accompanying table on independent random samples from each school, test to see if evidence exists of a difference between \(\mu_{1}\) and \(\mu_{2}\). Use .
School I |
School II |
School III |
\(\Sigma x_{1}^{2}=36,950\) |
\(\Sigma y_{1}^{2}=25,850\) |
\(\Sigma w_{1}^{2}=49,900\) |
\(\bar{x}=60\) |
\(\bar{y}=50\) |
\(\bar{w}=70\) |
Equation transcription:
Text transcription:
mu{1}, mu{2}
mu{3}
sigma^{2}(sigma{1}^{2}=sigma{2}^{2}=\sigma{3}^{2}=\sigma^{2})
mu{1}
mu{2}
Sigma x{1}^{2}=36,950
Sigma y{1}^{2}=25,850
Sigma w{1}^{2}=49,900
bar{x}=60
bar{y}=50
bar{w}=70
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