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 and found that 320 were correct 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) Determine and interpret the P-value.

(e) Based on the P-value, what is the conclusion of the hypothesis test at a 0.05 level of significance?