SOLUTION: I have found a solution already but I am still having a problem with (b) in the problem. What formula do I use to find the answer. To test the hypothesis that students who fini

Question 180619: I have found a solution already but I am still having a problem with (b) in the problem.
What formula do I use to find the answer.
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. (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!
What formula do I use to find the answer 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
Ha: u(first) - u(later) > 0 (this for right-tailed test)
(b) Obtain a test statistic and p-value assuming equal variances.
Interpret these results.
test statistic: z = (77.1-69.3)/sqrt[(19.6)^2/25 + (24.9)^2/24] = 1.2152
p-value = P(z > 1.2152) = 0.112146...
Interpretation: At least 11.23% of test results could have provided stronger
evidence against Ho.
(c) Is the difference in mean scores large enough to be important?
Yes ; We reject the hypothesis that the two means are statistically equal.

(d) Is it reasonable to assume equal variances?
If your text treats that question you need to look at the explanation.
(e) Carry out a formal test for equal variances at α = .05, showing
all steps clearly.
Ho: s^2(first) = s^2(later)
Ha: s^2(first) is not equal to s^2(later)
---------
F-statistic = (24.9)^2/(19.6)^2 =1.6139...
Critical Value:
df Numerator = (25-1) = 24
df Denominator= (24-1) = 23
Using F chart critical value = 2.03
----
Conclusion: Since test statistic < F-statistic Fail to reject Ho.
The variances are statiscaly equal.
==========================================
Cheers,
Stan H.
I would appreciate knowing whether this is any help to you.

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