3. Alfredo thinks that he may have ESP. One experiment uses a shuffled deck of five cards in which each card has one of five different pictures on it (circle, cross, square, star and wave). A card is selected from the deck. The subject is asked to guess the picture of the selected card. After the response is recorded the card is returned to the deck and the deck is shuffled. If a subject does not have ESP, there is a better chance of a correct answer. Alfredo wishes to test the hypothesis Ho: P = 0.20 versus H1: P > 0.20. Alfredo participates in the experiment and is right in 36 out of 50 tries. At a = 0.01 test the hypothesis that Alfredo has ESP. (a) Find the p-value. (b) State your conclusion. (c) Explain why these data do not prove Alfredo has ESP. 4. Over the past few months a supervisor has been attempting to decrease the number of status reports having discrepancies by implementing a new check system. These reports are being submitted to Headquarters Accounting for inventory reconciliation. Before the new system was in place, about 20% of the reports submitted had discrepancies. A recent random sample of 40 reports revealed only 4 having discrepancies. We wish to assess whether the population proportion of reports with discrepancies has significantly decreased from the past rate, at a 5% significance level. (a) Give the statistical hypothesis. (b) Calculate the p-value. (c) Explain whether or not the null hypothesis should be rejected. (d) Are the data statistically significant at the required level of significance