Question

Infants weighing less than 1500 grams at birth are classed as "very low birth weight." Low birth weight carries many risks. One study followed 114 male infants with very low birth weight to adulthood. At age 20, the mean IQ score for these men was x = 87.1. IQ scores vary Normally with standard deviation σ = 13. Give a 95% confidence interval for the mean IQ score at age 20 for all very-low-birth-weight males. Use the four-step process for confidence intervals (page 342) as a guide. (Round your answers to two decimal places.)

Answer 1

Solution :

Given that,

= 87.1

= 13

n = 114

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.005 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * (13 / 144)

= 2.12

At 95% confidence interval for the mean IQ score at age 20 for all very-low-birth-weight males.

- E < < + E

87.1 - 2.12 < < 87.1 + 2.12

84 .98< < 89.22

(84 .98 , 89.22 )