The scores of a certain population on the Wechsler Intelligence Scale for Children IV (WISC IV) are thought to be Normally distributed, with mean μ and standard deviation σ= 15. Bill is a child psychologist who obtains a simple random sample of 25 children from this population; each child is given the WISC IV. The mean of the 25 scores is x̄= 104.32. Based on these data, what is the margin of error for a 95% confidence interval for μ?

Question

Quizplus · Accepted Answer

The margin of error formula for a 95% confidence interval is: 
Margin of error = 1.96 * (standard deviation / square root of sample size)

We are given that σ = 15 and n = 25. So, 
Margin of error = 1.96 * (15 / sqrt(25)) 
Margin of error = 1.96 * (15 / 5) 
Margin of error = 1.96 * 3 
Margin of error = 5.88

Therefore, the margin of error for a 95% confidence interval for μ is approximately 5.88, which corresponds to choice C.

The Scores of a Certain Population on the Wechsler Intelligence