The Weschler Intelligence Scale for Children (WISC) is an intelligence test designed for children between the ages of 6 and 16. The test is standardized so that the mean score for all children is 100 and the standard deviation is 15. Suppose that the administrators of a very large and competitive school district wish to estimate the mean WISC score for all students enrolled in their programs for gifted and talented children. They obtained a random sample of 40 students currently enrolled in at least one program for gifted and talented children. The test scores for this sample are as follows: 106 142 110 123 135 114 119 118 121 95 154 119 109 131 130 98 117 105 143 94 110 167 117 98 125 133 122 98 116 126 127 114 124 134 133 102 125 109 124 109 Click to download the data in your preferred format. Use this data to calculate the mean WISC score, ?⎯⎯⎯, for these 40 students. Next, compute the standard deviation, SD, of the sampling distribution of the sample mean, assuming that the standard deviation of WISC scores for students in the district is the same as for the population as a whole. Finally, determine both the lower and upper limits of a 95% ?-confidence interval for ?, the mean score for all students in the school district who are enrolled in gifted and talented programs. Give ?⎯⎯⎯ and the limits of the confidence interval precise to one decimal place, but give the standard deviation to at least three decimal places in order avoid roundi
The Weschler Intelligence Scale for Children (WISC) is an intelligence test designed for children between the ages of 6 and 16. The test is standardized so that the mean score for all children is 100 and the standard deviation is 15.
Suppose that the administrators of a very large and competitive school district wish to estimate the mean WISC score for all students enrolled in their programs for gifted and talented children. They obtained a random sample of 40 students currently enrolled in at least one program for gifted and talented children. The test scores for this sample are as follows:
| 106 | 142 | 110 | 123 | 135 | 114 | 119 | 118 | 121 | 95 | 154 | 119 | 109 | 131 | 130 | 98 | 117 | 105 | 143 | 94 |
| 110 | 167 | 117 | 98 | 125 | 133 | 122 | 98 | 116 | 126 | 127 | 114 | 124 | 134 | 133 | 102 | 125 | 109 | 124 | 109 |
Click to download the data in your preferred format.
Use this data to calculate the mean WISC score, ?⎯⎯⎯, for these 40 students. Next, compute the standard deviation, SD, of the sampling distribution of the sample mean, assuming that the standard deviation of WISC scores for students in the district is the same as for the population as a whole. Finally, determine both the lower and upper limits of a 95% ?-confidence interval for ?, the mean score for all students in the school district who are enrolled in gifted and talented programs.
Give ?⎯⎯⎯ and the limits of the confidence interval precise to one decimal place, but give the standard deviation to at least three decimal places in order avoid rounding errors when computing the limits.
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