6.3.26 (One-sided hypotheses for means ) Suppose that (x1,..., xn) is a sample from a N(, ?2 0) distribution, where is unknown and ?2 0 is known. Suppose we want to assess the hypothesis H0 : ? 0. Under these circumstances, we say that the observed value x is surprising if x occurs in a region of low probability for every distribution in H0. Therefore, a sensible P-value for this problem is max?H0 P(X > x). Show that this leads to the P-value 1 ? 4((x ? 0)/(?0/ ?n)). 6.3.27 Determine the form of the power function associated with the hypothesis assessment procedure of Problem 6.3.26, when we declare a test result as being statistically significant whenever the P-value is less than ?.

6.3.26 (One-sided hypotheses for means ) Suppose that (x1, .. ., Xn) is a sample from a N(u, ) distribution, where u is unknown and o is known. Suppose we want to assess the hypothesis Ho : u x). Show that this leads to the P-value 1 - P((x - Mo)/(o0/ n)). 6.3.27 Determine the form of the power function associated with the hypothesis assess- ment procedure of Problem 6.3.26, when we declare a test result as being statistically significant whenever the P-value is less than a