In the situation of Example 8 5 11, suppose that we observe X1 4 7 and X2 5 3 a Find the 50 confidence interval described in Example 8 5 11 b Find the interval of possible values that are consistent with the observed data c Is the 50 confidence interval larger or smaller than the set of possible va...

a The interval between the smaller an larger values is 47 53 b The values of consistent with the observed data are those between 53 05 48 and 47 05 52 c The interval in part a contains the set of all possible values hence it is larger than the set of possible values d The value ...

In the situation of Example 8.5.11, suppose that we observe X1 = 4.7 and X2 = 5.3.

Question:

In the situation of Example 8.5.11, suppose that we observe X1 = 4.7 and X2 = 5.3.
a. Find the 50% confidence interval described in Example 8.5.11.
b. Find the interval of possible θ values that are consistent with the observed data.
c. Is the 50% confidence interval larger or smaller than the set of possible θ values?
d. Calculate the value of the random variable Z = Y2 − Y1 as described in Example 8.5.11.
e. Use Eq. (8.5.15) to compute the conditional probability that |2 − θ| < 0.1 given Z equal to the value computed in part (d).