A group of students take a math test. To test if sleep has an effect on their performance, they get 8 hours of sleep for 2 weeks each night, and then take the same math test again. Their scores are listed below. Did sleep have a significant different on their math test performance? (alpha=0.05)
Math Test 1 |
Math Test 2 |
84 |
86 |
95 |
95 |
53 |
70 |
96 |
98 |
82 |
86 |
79 |
75 |
68 |
78 |
93 |
95 |
Find the sum of the difference scores and the mean of the difference scores.
Σ= 33 Mean D = 4.125 |
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Σ= -33 Mean D = -4.125 |
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Σ= 433 Mean D = -4.125 |
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Σ= 33 Mean D = -5.30 |
Find the variance of the difference scoress
S^{2}_{D=42.41} |
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S^{2}_{D=433} |
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S^{2}_{D=50.00} |
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S^{2}_{D=296} |
Find the standard error of the mean difference
S_{D} = 5.30 |
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S_{D = 6.00} |
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S_{D = 2.30} |
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S_{D= 42.41} |
Calculate the t-statistic
t = 1.79 |
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t = -1.79 |
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t = .77 |
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t= -.77 |
Find the t-critical value
+/- 2.365 |
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+/- 2.447 |
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+/-2.306 |
What decision should you make concerning the null hypothesis?
Fail to reject the null hypothesis, because the t-statistic is greater than the t-critical value |
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Fail to reject null hypothesis, because the t-statistic is less than the t-critical value |
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Reject the null hypothesis, because the t-statistic is less than the t-critical value |
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Reject the null hypothesis, because the t-statistic is greater than the t-critical value |
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