6-1. A study is run to estimate the mean total cholesterol level in children 2 to 6 years of age. A sample of 9 participants is selected and their total cholesterol levels are measured as follows:

185 225 240 196 175 180 194 147 223

Generate a 95% confidence interval for the true mean total cholesterol levels in children

Mean = (185+225+240+196+175+180+194+147+223)/9 = 196.11

Sample standard deviation = S = Σ(Xi - μ)2 / (N-1) = 29.00

Since both standard deviation and sample mean are unknown so we will use chi-square distribution. we will use a t- distribution with 8 degrees of freedom

t.025,8 = 2.306

so -2.306<√8(X” - μ)/S<2.306

172.47 < X” < 219.75

Where X” is the sample mean