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): 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) P(A)+ C)-P P(B (Anz (A) gers -(- n 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