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The WAIS is a standardized IQ test with a verbal and a non-verbal “performance" component, which separately measure language-related (e.g., vocabulary) and non- language related skills (e.g., reasoning about numerical quantity). The tests have been extensively normed, and the mean Verbal IQ (VIQ) and Performance IQ (PIQ) scores are µviQ=µPiQ=100, and both tests have a standard deviation of o=15. The Full Scale IQ (FSIQ) is calculated by averaging these two subtests, and is used as an indicator of general cognitive ability. The FSIQ score also has a population mean of µfsiQ=100 and o=15.

The WAIS is a standardized IQ test with a verbal and a non-verbal “performance" component, which separately measure language-related (e.g., vocabulary) and non- language related skills (e.g., reasoning about numerical quantity). The tests have been extensively normed, and the mean Verbal IQ (VIQ) and Performance IQ (PIQ) scores are µviQ=µPiQ=100, and both tests have a standard deviation of o=15. The Full Scale IQ (FSIQ) is calculated by averaging these two subtests, and is used as an indicator of general cognitive ability. The FSIQ score also has a population mean of µfsiQ=100 and o=15.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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The WAIS is a standardized IQ test with a verbal and a non-verbal “performance” component, which separately measure language-related (e.g., vocabulary) and non-language related skills (e.g., reasoning about numerical quantity). The tests have been extensively normed, and the mean Verbal IQ (VIQ) and Performance IQ (PIQ) scores are \( \mu_{VIQ} = \mu_{PIQ} = 100 \), and both tests have a standard deviation of \( \sigma = 15 \). The Full Scale IQ (FSIQ) is calculated by averaging these two subtests, and is used as an indicator of general cognitive ability. The FSIQ score also has a population mean of \( \mu_{FSIQ} = 100 \) and \( \sigma = 15 \). Statistical criteria are applied to these test scores to diagnose general cognitive impairment or a specific learning disorder like dyslexia (difficulty reading) or dyscalculia (difficulty with mathematical reasoning). 7. Social services are available to those who meet a threshold of cognitive impairment. In some states, those with an FSIQ score of less than 76 meet this threshold. What proportion of the population in these states meets this criterion? 8. A school district in WNY has 20,000 students in any given year. Of these students, those with very high or very low IQ scores (FSIQ > 124 or FSIQ < 76) are enrolled in specialized programs. How many students in the district would we expect are not enrolled in specialized programs in a given year? 9. Specific learning disorders like Dyslexia are diagnosed by a discrepancy between the scores on the IQ subtests. For example, a student with low VIQ score but a normal or high PIQ score might be diagnosed with a specific language impairment. In one school district, any PIQ or VIQ score above 89 is considered to be in the normal range; scores below that cutoff are classified as “low”. What proportion of the population has a discrepancy diagnosis indicating a language impairment (a low VIQ score and a normal PIQ score)?
Transcribed Image Text:The WAIS is a standardized IQ test with a verbal and a non-verbal “performance” component, which separately measure language-related (e.g., vocabulary) and non-language related skills (e.g., reasoning about numerical quantity). The tests have been extensively normed, and the mean Verbal IQ (VIQ) and Performance IQ (PIQ) scores are \( \mu_{VIQ} = \mu_{PIQ} = 100 \), and both tests have a standard deviation of \( \sigma = 15 \). The Full Scale IQ (FSIQ) is calculated by averaging these two subtests, and is used as an indicator of general cognitive ability. The FSIQ score also has a population mean of \( \mu_{FSIQ} = 100 \) and \( \sigma = 15 \). Statistical criteria are applied to these test scores to diagnose general cognitive impairment or a specific learning disorder like dyslexia (difficulty reading) or dyscalculia (difficulty with mathematical reasoning). 7. Social services are available to those who meet a threshold of cognitive impairment. In some states, those with an FSIQ score of less than 76 meet this threshold. What proportion of the population in these states meets this criterion? 8. A school district in WNY has 20,000 students in any given year. Of these students, those with very high or very low IQ scores (FSIQ > 124 or FSIQ < 76) are enrolled in specialized programs. How many students in the district would we expect are not enrolled in specialized programs in a given year? 9. Specific learning disorders like Dyslexia are diagnosed by a discrepancy between the scores on the IQ subtests. For example, a student with low VIQ score but a normal or high PIQ score might be diagnosed with a specific language impairment. In one school district, any PIQ or VIQ score above 89 is considered to be in the normal range; scores below that cutoff are classified as “low”. What proportion of the population has a discrepancy diagnosis indicating a language impairment (a low VIQ score and a normal PIQ score)?
Expert Solution
Step 1

From the given information,

The FSIQ score also has a population mean of μFSIQ=100 and σ=15.

Let us define X as the FSIQ score follows Normal with μFSIQ=100 and σ=15.

 

7.

The proportion of the population in the states meets the criterion is,

PX<76=PX-μσ<76-μσ                 =Pz<76-10015                =Pz<-1.6               =0.0548, from the standard normal table

 

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