Suppose that the weights (in kgs) of six months old babies, monitored at a healthcare facility, have
N(μ,σ2) distribution, where
μ∈R and
σ>0 are unknown parameters. Let
X1,X2,…,X9 be a random sample of the weights of such babies. Let
X=91∑i=19Xi,
S=81∑i=19(Xi−X)2 and let a 95% confidence interval for
μ based on
t-distribution be of the form
(X−h(S),X+h(S)), for an appropriate function
h of random variable
S. If the observed values of
X and
S2 are 9 and 9.5, respectively, then the width of the confidence interval is equal to __________ (round off to 2 decimal places) (You may use
t9,0.025=2.262,t8,0.025=2.306,t9,0.05=1.833,t8,0.05=1.86).