The data you will be analyzing are on educational transitions for a sample of 470 Irish schoolchildren aged 11 in 1967. Focus on the variable DVRT (Drumcondra Verbal Reasoning Test Score) only. Make sure that when you do analysis you are analyzing this variable and not another mistakenly. Using the data provided, answer the following questions and provide the requested analysis.

1) Assuming the DVRT scores are an iid sample from a Normal distribution, what is the 'best' unbiased estimator of the population mean, ? Report the estimated value for the DVRT data using this estimator? - 3/4 pt

2) Similarly, assuming the DVRT scores are an iid sample from a Normal distribution, what is the 'best' unbiased estimator of the variance for the population, 2? Report the estimated value for the DVRT data using this estimator? - 3/4 pt

3) The answers to parts (1) & (2) relied on the assumption that the data could be approximated by the iid Normal model (i.e. an iid sample from some Normal distribution). Identify a way to check this assumption and carry out your suggested method on the data. Comment on whether the Normal model is reasonable for this data. - 1.5 pt

4) Construct a 95% Confidence Interval for the typical DVRT score in the population. - 2 pts

Data:

DVRT

113

101

110

121

82

85

84

98 92 90 88 84 114 70 109 83 108 95 90 107 86 70 114 117 112 88 106 125 94 103 123 100 90 70 90 99 123 127 124 110 94 112 123 70 102 126 121 100 85 86 101 91 113 103 117 72 70 112 65 97 100 99 91 107 94 104 117 104 115 123 103 109 99 100 100 107 70 91 117 115 93 103 99 115 104 116 94 114 113 106 119 114 108 97 83 103 104 97 109 90 114 99 94 86 93 91 109 91 106 109 111 111 106 86 107 103 100 101 97 105 98 111 88 123 98 94 109 70 75 72 70 70 70 70 85 108 75 104 103 122 110 107 104 70 116 103 95 113 126 118 115 89 113 85 95 109 111 116 90 90 82 84 117 71 104 86 79 80 99 86 116 124 98 101 87 97 120 103 107 105 99 103 101 102 105 70 101 90 85 104 87 85 102 94 93 99 103 89 77 92 109 91 109 105 105 90 99 110 88 101 91 78 118 100 100 85 106 70 97 86 92 102 86 78 100 104 70 107 114 103 115 106 114 90 103 92 113 92 108 96 70 112 106 91 96 70 109 74 99 107 90 78 70 88 93 88 108 101 98 103 73 109 102 93 93 101 100 70 102 113 91 109 80 118 70 88 72 81 70 97 87 99 81 84 90 95 84 104 105 107 84 108 70 99 87 81 103 114 101 70 70 109 78 70 70 104 86 99 98 118 76 102 106 108 110 110 89 83 96 113 95 108 96 79 99 107 94 88 82 100 102 111 111 94 94 93 90 84 100 106 114 101 115 108 117 110 93 114 72 116 117 102 84 94 81 101 91 93 116 90 115 89 108 100 86 84 90 103 100 102 82 83 113 117 111 100 91 97 109 100 98 85 91 85 81 87 95 102 94 89 112 118 70 103 90 97 104 91 94 107 90 70 97 104 96 81 114 106 105 92 96 84 89 111 102 99 104 70 70 90 104 102 86 73 81 93 111 104 105 73 85 107 112 127 114 114 109 93 114 100 92 110 93 96 120 114 127 106 110 92 125 108 112 93 114 104 92 104 109 109 104 123 125 127 129 119 125 121 124 125 129 122 121 129 122 126 122 123 119 120 127 127 120 127 123 120 123 122 119 130 134 136 135 140 131 137 136 132 135 134