SOLUTION: To test the hypothesis that students who finish an exam first get better grades, Professor Hardtack kept track of the order in which papers were handed in. The first 25 papers hand

Question 263860: To test the hypothesis that students who finish an exam first get better grades, Professor Hardtack kept track of the order in which papers were handed in. The first 25 papers handed in showed a mean score of 77.1 with a standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9. Is this a significant difference a α = .05? a)State the hypothesis for a right-tailed test. b)Obtain a test statistic and p-value assuming equal variances. Interpret these results. c)Is the difference in mean scores large enough to be important? d)Is it reasonable to assume equal variances? e)Carry out a formal test for equal variances at α = .05, showing all steps clearly.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
To test the hypothesis that students who finish an exam first get better grades, Professor Hardtack kept track of the order in which papers were handed in.
The first 25 papers showed a mean score of 77.1 with a standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9.
Is this a significant difference at α = .05?
(a) State the hypotheses for a right-tailed test.
Ho: u(first) - u(later) = 0
H1: u(first) - u(later) > 0
-----------------------------
(b) Obtain a test statistic and p-value assuming equal variances. Interpret these results.
I ran a 2-sample t-Test and got the following:
test statistic: t = 1.2152
p-value = 0.1154:
Interp: 11.54% of test results could have provided stronger evidence for
rejecting Ho.
-----------------------------
(c) Is the difference in mean scores large enough to be important?
No ; Fail to reject Ho
-----------------------------
(d) Is it reasonable to assume equal variances?
I'll leave that to you.
-----------------------------
(e) Carry out a formal test for equal variances at α = .05, showing all steps clearly.
test statistic F = 24.9^2/19.6^2 = 1.6139
--------------
Critical value: F = 2.23
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Conclusion: Fail to reject Ho.
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Cheers,
Stan H.

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