The Weschler Intelligence Scale for Children (WISC) is an intelligence test desi

Question

The Weschler Intelligence Scale for Children (WISC) is an intelligence test designed for children between the ages of 6 and the standard deviation is 15. Suppose that a very large and competitive school district, administrators 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 in at least one program for gifted and talented children. The test scores 137,112, 112,147, 131,129. 122,114,117, 132, 108, 99, 105, 133, 114,105, 117, 104,91.119, 109, 134, 109, 130, 111, 102, 140, 127, 114, 118, 124, 122, 138, 121, 122, 117, 117, 134, 137, 126

Explanation / Answer

TRADITIONAL METHOD
given that,
sample mean, x =120
standard deviation, s =12.62
sample size, n =40
I.
stanadard error = sd/ sqrt(n)
where,
sd = standard deviation
n = sample size
standard error = ( 12.62/ sqrt ( 40) )
= 2
II.
margin of error = t /2 * (stanadard error)
where,
ta/2 = t-table value
level of significance, = 0.01
from standard normal table, two tailed value of |t /2| with n-1 = 39 d.f is 2.708
margin of error = 2.708 * 2
= 5.4
III.
CI = x ± margin of error
confidence interval = [ 120 ± 5.4 ]
= [ 114.6 , 125.4 ]
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DIRECT METHOD
given that,
sample mean, x =120
standard deviation, s =12.62
sample size, n =40
level of significance, = 0.01
from standard normal table, two tailed value of |t /2| with n-1 = 39 d.f is 2.708
we use CI = x ± t a/2 * (sd/ Sqrt(n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
CI = confidence interval
confidence interval = [ 120 ± t a/2 ( 12.62/ Sqrt ( 40) ]
= [ 120-(2.708 * 2) , 120+(2.708 * 2) ]
= [ 114.6 , 125.4 ]
-----------------------------------------------------------------------------------------------
interpretations:
1) we are 99% sure that the interval [ 114.6 , 125.4 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 99% of these intervals will contains the true population mean

SE = 2, LCL = 114.6 , UCL = 125.4

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