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The Weschler Intelligence Scale for Children (WISC) is an intelligence test designed for children between the...

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: 94,106,123,111,127,112,132,107,123,115,133,132,121,109,121,110,107,128,104,118, 111,127,108,119,121,122,102,130,97,111,125,114,99,101,123,124,108,116,144,113 Click to download the data in your preferred format. CrunchIt! CSV Excel JMP Mac Text Minitab PC Text R SPSS TI Calc 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 90% ?-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.

x=

SD =

Lower limit =

Upper limit =

Solutions

Expert Solution

Following table shows the calculations:

X (X-mean)^2
94 492.84
106 104.04
123 46.24
111 27.04
127 116.64
112 17.64
132 249.64
107 84.64
123 46.24
115 1.44
133 282.24
132 249.64
121 23.04
109 51.84
121 23.04
110 38.44
107 84.64
128 139.24
104 148.84
118 3.24
111 27.04
127 116.64
108 67.24
119 7.84
121 23.04
122 33.64
102 201.64
130 190.44
97 368.64
111 27.04
125 77.44
114 4.84
99 295.84
101 231.04
123 46.24
124 60.84
108 67.24
116 0.04
144 772.84
113 10.24
Total 4648 4860.4

-------------------------------

x-bar=116.2

SD = 11.1636

Lower limit = 113.3

Upper limit = 119.1

orchestra answered 1 year ago
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