Females participated in every event at the 2012 Summer Olympic Games. Prior to 2012, there had been a steady increase in the female participation rate. The International Olympic Committee states that the female participation in the 2004 Summer Olympic Games was 42%, even with new sports such as weightlifting, hammer throw, and modern pentathlon recently added to the Games. Prior to the 2008 Games, an independent sport expert arranged for a random sample of pre-Olympic exhibitions. The sports expert reported that 202 of 454 athletes in the random sample were women. Is this strong evidence that the participation rate may have increased? Use =0.05. a. State the hypotheses in symbols. (2 points) b. Check the assumptions to make sure all conditions are met. Provide a full explanation of each assumption and how this problem meets them. (2 points) c. Run the required test and provide the test statistic and P-value. Don't forget to write your calculator commands. (4 points) d. Write a full conclusion for this test in the context of the problem. Your conclusion should say, "Since the P-value is (above or below) the significance level of 0.05, we (reject or fail to reject) the null hypothesis and conclude that there (is or is not) enough evidence to suggest that (make a statement using the context of the problem)." (2 points) e. Find a 90% confidence interval for the proportion of female athletes in this sample. Be sure to write out your calculator commands. (2 points) f. Does this confidence interval support your conclusion in part d? Explain.