Here are the IQ scores for the 15 first-grade girls from the study mentioned in Example 15.9.

Assume that the data is a random sample from a normal distribution with mean µ and σ = 15, and assign to l the same N(110, 7.5) prior distribution used in Example 15.9.

a. Determine the posterior distribution of µ.
b. Calculate and interpret a 95% credible interval for µ.
c. Add four observations with average 110 to the data and compute a 95% confidence one-sample z interval for µ using the 19 observations. Compare with the result of (b).
d. Change the prior so the prior precision is very small but positive, and then recompute (a) and (b).

e. Calculate a 95% confidence one-sample z interval for µ using the 15 observations and compare with the credible interval of (d).

Transcribed Image Text:

102 109 113 96 106 118 108 82 110 121 122 110 115 99 113