Janeane Garofalo
IQ: 104 ± 18
🔍 How Did We Calculate This?
Note: Janeane Garofalo's SAT score is 950, which we utilized for our IQ estimate.
1️⃣ SAT to IQ Conversion:
Utilizing the formula IQ = 39.545 + 0.068 × SAT score, we estimated her IQ to be around 104.
2️⃣ Calculating the Standard Error:
The correlation between SAT scores and IQ is 0.8. The unexplained variance is 20%, calculated as 1 - r² (where r is the correlation coefficient). We calculate the standard error (SE) as SE = SD × √(1 - r²), where SD is the standard deviation of IQ scores (15). This calculation results in an SE of approximately 9.
3️⃣ Determining the Margin of Error:
For a 95% confidence interval, the z-score is 1.96. We calculate the margin of error (MOE) using MOE = z * SE. Therefore, MOE = 1.96 × 9 ≈ 18.
4️⃣ Final Result:
The 95% confidence interval is determined by adding and subtracting the MOE from the estimated IQ. Hence, Janeane Garofalo's IQ is estimated to be 104 with a 95% confidence interval of approximately 104 ± 18, translating to a range from about 87 to 122.