In his book, "The Signal and the Noise," Nate Silver analyzed 733 predictions made by experts regarding political events. Of the 733 predictions, 338 were mostly true.

(a)Determine the sample proportion of political predictions that were mostly true.

(b)Suppose that we want to know whether the evidence suggests the political predictions were mostly true less than half the time. State the null and alternative hypotheses.

(c)Verify the normal model may be used to determine the P-value for this hypothesis test.

(d)Draw a normal model with the area representing the P-value shaded for this hypothesis test.

(e)Determine the P-value based on the model from part (d).

(f)Interpret the P-value.

(g)Based on the P-value, what does the sample evidence suggest? That is, what is the conclusion of the hypothesis test? Assume an a = 0.1 level of significance. State the conclusion based on the results of the test.