SOLUTION: 4. A teacher wishes to determine whether his brightest students (those making the best grades) tend to turn in their tests earlier (because they can recall the material faster) or

Question 590751: 4. A teacher wishes to determine whether his brightest students (those making the best grades) tend to turn in their tests earlier (because they can recall the material faster) or later (because they take longer to write down all they know) than the others in the class. For a particular test, he observes that the students make the following grades in order of turning their tests in:
Order Grades
1-10 94 70 85 89 92 98 63 88 74 85
11-20 69 90 57 86 79 72 80 93 66 74
21-30 50 55 47 59 68 63 89 51 90 88
If the teacher counts those making a grade of 90 and above as his brightest students, then at a 5 percent level of significance, can he conclude the brightest student turned their tests in randomly?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A teacher wishes to determine whether his brightest students (those making the best grades) tend to turn in their tests earlier (because they can recall the material faster) or later (because they take longer to write down all they know) than the others in the class. For a particular test, he observes that the students make the following grades in order of turning their tests in:
Order Grades
1-10 94 70 85 89 92 98 63 88 74 85::::::
Proportion of high marks = 3/10
Expected proportion: 2/10
--------------------------------------------------
11-20 69 90 57 86 79 72 80 93 66 74:::::
Proportion of high marks = = 2/10
Expected proportion: 2/10
--------------------------------------------------
21-30 50 55 47 59 68 63 89 51 90 88:::::
Proportion of high marks = 1/10
Expected proportion: 2/10
If the teacher counts those making a grade of 90 and above as his brightest students, then at a 5 percent level of significance, can he conclude the brightest student turned their tests in randomly?
-----
Ho: The proportions are the same
Ha: At least one of the proportions is different
---
I ran a Chi-Sq Goodness-of-Fit Test and got:
Chi-Sq = 1.3333
p-value = 0.72
---
Since the p-value is greater than 5%, fail to reject
Ho at the 5% level of confidence.
=====================
Cheers,
Stan H.

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