(19.36) Infants weighing less than 1500 grams at birth are classed as very low b

Question

(19.36) Infants weighing less than 1500 grams at birth are classed as very low birth weight. Low birth weight carries many risks. One study followed 113 male infants with very low birth weight to adulthood. At age 20, the mean IQ score for these men was x = 87.6. IQ scores vary Normally with standard deviation = 15. Give a 95% confidence interval for the mean IQ score at age 20 for all very-low-birth-weight males. Step 1: STATE: What is the question to be answered? How many very-low-birth-weight males are retarded? What is the mean IQ of 20 years old very-low-birth-weight males? What risks does very-low-weight birth carry? Are very-low-birth-weight males retarded? Step 2: FORMULATE: How will we estimate the parameter? We will estimate the mean IQ of all very-low-birth-weight males by giving a 90% confidence interval. We will estimate the mean IQ of all very-low-birth-weight males by giving a 90 confidence interval. We will estimate the mean IQ of all very-low-birth-weight males by giving a 95 confidence interval. We will estimate the mean IQ of all very-low-birth-weight males by giving a 95% confidence interval. Step 3: SOLVE: What is the confidence interval for the mean IQ of very-low-birth-weight males? 87.6 ± 3.6 87.6 ± 2.3 87.6 ± 2.8 87.6 ± 1.8 Step 4: CONCLUDE: What is your conclusion? We are 95% confident that the mean IQ of all very-low-birth-weight males is between 85.8 and 89.4. We are 95% confident that the mean IQ of all very-low-birth-weight males is between 85.3 and 89.9. We are 95% confident that the mean IQ of all very-low-birth-weight males is between 84 and 91.2. We are 95% confident that the mean IQ of all very-low-birth-weight males is between 84.8 and 90.4.

Explanation / Answer

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=87.6
Standard deviation( sd )=15
Sample Size(n)=113
Confidence Interval = [ 87.6 ± Z a/2 ( 15/ Sqrt ( 113) ) ]
= [ 87.6 - 1.96 * (1.41) , 87.6 + 1.96 * (1.41) ]
= [ 84.83,90.37 ]

[ASNWERS]
Mean = 87.6
We will estimate the mean IQ of all very-low-birth-weight males by giving a 95 confidence interval.
We are 95% confident that the mean IQ of all very-low-birth-weight males is between 84.8 and 90.4

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