Question

Researchers were interested in estimating the mean body mass index (BMI) for 5 year old girls in a very large school district in Oklahoma. A random sample of size 61 five year old girls was drawn, and the sample mean BMI was found to be 17.4. Although BMI measurements are typically a little right-skewed, because of the reasonably large sample size, the researchers felt it was reasonable to use procedures based on the normal distribution. Based on previous information, they felt it was reasonable to believe the population standard deviation of σ=3.8.

a) What is the margin of error for a 95% confidence level for mu, the true mean BMI for five-year old girls in this school district?

Round your response to at least 3 decimal places.

b) What is the margin of error for a 90% confidence level?

Round your response to at least 3 decimal places.

Answer 1

Page No. Date: / / Solution!- Given that, x= 17.4 6- 3.8 n=61 g) At a solo confidence level, L= 1-95 % del-0.05 -0.05 -0.05 -0.025 2012 – 20.025 = 1.96 Margin of errorze = 2012 x6 un E=1.96 x 3-8 - VG E- 0.954 At as lo confidence interalis, - X-EC Mc XtE 17.4 -0.954 CM 17.4 to.954 16.446 <al< 18.354 116,446, 18:354]

Page No. Date: level b) At qa olo confidence x=1- 98 % . dol-0.90 = 0.10 = 0;L0 = 0.05 2212= Zo.o5 -1.045 Margin of error=E=2212x & E= 1.645 * 3.8 161 __ E=0.800 Margin of error = E=0.800