Question

A group of researchers developed a 95% z confidence interval for the mean body mass index (BMI) of women aged 20 to 29 years, based on a national random sample of 647 such women. They assumed that the population standard deviation was known to be σ = 7.5. In fact, the sample data had mean BMI x = 26.9 and standard deviation s = 7.39. What is the 95% tconfidence interval for the mean BMI of all young women? (Round your answers to three decimal places.)

Answer: ___ to ____

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 26.9

Population standard deviation =    = 7.5

Sample size = n = 647

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= 1.96 * ( 7.5 /  647 )

= 0.578

At 95% confidence interval estimate of the population mean is,

  ± E

26.9 ± 0.578

( 26.322 to 27.478 )