Homework SourseThe following data are from a hypothetical study on the effe
The following data are from a hypothetical study on the effects of age and time on scores on a test of reading comprehension. Compute the analysis of variance summary table.
12-year olds
16-year olds
30 minutes
66
68
59
72
46
74
71
67
82
76
60 minutes
69
61
69
73
61
95
92
95
98
94
| 12-year olds | 16-year olds | |
| 30 minutes | 66 68 59 72 46 | 74 71 67 82 76 |
| 60 minutes | 69 61 69 73 61 | 95 92 95 98 94 |
Solution
The Variance is defined as: The average of the squared differences from the Mean.
The variance of a sample is defined by slightly different formula:
s2 = ( xi - x )2 / ( n - 1 )
by applying the formula of mean that is sum of all observation divided by total observation
we can get the required variance from the formula given above.
12 years 30 min 12 years 60 min
Mean (x): 62.2 Sample size:5
Variance (s2): 104.2 Mean (x): 66.6
Variance (s2): 28.8
analysis = improvement of students increased in 60 minute test but not much.
16 years 30 min 16 years 30 min
Mean (x): 74 Mean (x): 94.8
Variance (s2): 31. 5 Variance (s2): 4.7000000000007
analysis = in this the mean increased considerably from 30 min to 60 min
