Problem 8) During the refurbishment of a bakery, a new cake display was installed. Before the refurbishment, 20% of the customers bought cakes. The store manager claims that the proportion of customers buying cakes has now increased. He selects a random sample of 120 customers and finds that 30 of them have bought cakes. a) Test the store manager's claim using a = 0.10. using rejection regions. (Show work). State Null and Alternative Hypotheses (2 points): P(A)+ C)-P P(B "(A) gers -(- n Obtain Critical value(s) (2 points) (Round your answer to 2 decimal places).: Obtain Test Statistic (2 points) (Round your answer to 2 decimal places): Interpretation and Conclusion: Circle only one (1 point) i) Reject the null hypothesis ii) Fail to reject the null hypothesis Why? (2 points) Is there enough evidence to support the store manager's claim? Circle only one (1 point): i) Yes, there is enough evidence at a = 0.10 to support the manufacturer's claim ii) No, there is not enough evidence at a =0.10 to support the manufacturer's claim b) Obtain the P-value for the test above (4 points). (Round your answer to 4 decimal places). (Show work). t