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Suppose that ten girls aged 18 had both their heights and weights measured. Their heights in cm are as follows: 169.6 166.8 157.1 181.1 158.4 165.6 166.7 156.5 168.1 165.3 We assume that heights are normally distributed with an unknown mean µ and a known variance 50. Two individuals gave the following prior distributions for the mean height: Individual 1: µ ∼ N(165,22) Individual 2: µ ∼ N(170,32) Q. Calculate a classical 95% confidence interval for µ (from the frequentist approach) and a 95% credible interval for µ (from the Bayesian approach) for each individual. How are they compared? Make sure that you use a variance-known version of a confidence interval. A 100(1−α)% credible interval for µ is [ α/2 quantile, 1−α/2 quantile] of the posterior distribution of µ.

          Suppose that ten girls aged 18 had both their heights and weights measured. Their heights in cm are as follows:
169.6 166.8 157.1 181.1 158.4 165.6 166.7 156.5 168.1 165.3
We assume that heights are normally distributed with an unknown mean µ and a known variance 50. Two individuals gave the following prior distributions for the mean height:
Individual 1: µ ∼ N(165,22)
Individual 2: µ ∼ N(170,32) 
Q. Calculate a classical 95% confidence interval for µ (from the frequentist approach) and a 95% credible interval for µ (from the Bayesian approach) for each individual. How are they compared? Make sure that you use a variance-known version of a confidence interval.
A 100(1−α)% credible interval for µ is [ α/2 quantile, 1−α/2 quantile] of the posterior distribution of µ.

Added by Bonnie W.

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