The website pundittracker.com keeps track of predictions made by individuals in finance, politics, sports, and entertainment. Jim Cramer is a famous TV financial personality and author. Pundittracker monitored 678 of his stock predictions (such as a recommendation to buy the stock) and found that 320 were correct predictions. Treat these 678 predictions as a random sample of all of Cramer's predictions.

(a)Determine the sample proportion of predictions Cramer got correct.

(b)Suppose that we want to know whether the evidence suggests Cramer is correct 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 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 = 0.05 level of significance.