a-pediatrician-measures-head-circumferences-in-cm-of-1212-healthy-newborns-and-f

Question

A pediatrician measures head circumferences (in units of cm) of 1212 healthy newborns and finds a sample standard deviation of s=0.49s=0.49 cm. To gauge the precision of this estimate, she takes 1010 bootstrap samples (with the replacement) of size 1212 and computes each sample’s standard deviation. The sorted bootstrap standard deviations (in cm) are: 0.45,0.48,0.49,0.50,0.51,0.52,0.54,0.56,0.58,0.600.45,0.48,0.49,0.50,0.51,0.52,0.54,0.56,0.58,0.60. Using these 1010 values, construct a 95%95\% bootstrap confidence interval for the true population standard deviation σ\sigma.

Accepted Answer

0.45cm⁡≤σ≤0.60cm⁡0.45\operatorname{\mathrm{cm}}\le\sigma\le0.60\operatorname{\mathrm{cm}}

Answer

0.55cm⁡≤σ≤0.80cm⁡0.55\operatorname{\mathrm{cm}}\le\sigma\le0.80\operatorname{\mathrm{cm}}

Answer

0.45cm⁡≤σ≤0.80cm⁡0.45\operatorname{\mathrm{cm}}\le\sigma\le0.80\operatorname{\mathrm{cm}}

Answer

0.55cm⁡≤σ≤0.60cm⁡0.55\operatorname{\mathrm{cm}}\le\sigma\le0.60\operatorname{\mathrm{cm}}