To test the hypothesis that students who finish an exam ...
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 a = .05?
(a) State the hypotheses for a right-tailed test.
Hypotheses: H0: μ1 = μ2
Ha: μ1 > μ2
(b) Obtain a test statistic and p-value assuming equal variances. Interpret these results.
Given that for first 25 papers showed a mean score of 77.1 with a standard deviation of 19.6. N1 = 25, mean1 = 77.1 and Std.dev1 = 19.6
For last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9
N2 = 24, mean2 = 69.3, and Std.dev2 = 24.9
T = (77.1- 69.3)/ SQRT {[19.62 / 25] + [24.92 /24]}
T = 1.22
P value= 0.114
Therefore p-value 0.114 > 0.05, we fail to reject H0.There is no sufficient evidence to conclude that students who finish an exam first get better grades at 5% level of significance.
(c) Is the difference in mean scores large enough to be important?
No, it isn’t large enough to be important
(d) Is it reasonable to assume equal variances?
Yes, it is reasonable to assume equal variances
(e) Carry out a formal test for equal variances at a = .05
Ho: σ12 = σ22
Ha: σ12 ≠ σ22
F-statistic = 24.92 /19.62=1.614
Using F chart critical value = 2.3
Here test statistic < F-statistic Fail to reject Ho.
Therefore the variances are equal.
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